<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0" xmlns:itunes="http://www.itunes.com/dtds/podcast-1.0.dtd" xmlns:googleplay="http://www.google.com/schemas/play-podcasts/1.0"><channel><title><![CDATA[Parity: Telescope Editions]]></title><description><![CDATA[Frontier writing in the most exciting fields of our generation, including Blockchain, dWeb, AI, Robotics, Space Tech, Nuclear Energy, and Quantum Computing, as well as their extended topics like Digital Privacy, Autonomous Worlds, Space Exploration, and Internet Governance.]]></description><link>https://newsletter.parity.fund/s/telescope-editions</link><image><url>https://substackcdn.com/image/fetch/$s_!RbWh!,w_256,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F818e17c3-66a3-4064-bc93-6c68613d8cae_900x900.png</url><title>Parity: Telescope Editions</title><link>https://newsletter.parity.fund/s/telescope-editions</link></image><generator>Substack</generator><lastBuildDate>Sat, 07 Nov 2026 00:36:21 GMT</lastBuildDate><atom:link href="https://newsletter.parity.fund/feed" rel="self" type="application/rss+xml"/><copyright><![CDATA[Parity]]></copyright><language><![CDATA[en]]></language><webMaster><![CDATA[gm@parity.fund]]></webMaster><itunes:owner><itunes:email><![CDATA[gm@parity.fund]]></itunes:email><itunes:name><![CDATA[Parity]]></itunes:name></itunes:owner><itunes:author><![CDATA[Parity]]></itunes:author><googleplay:owner><![CDATA[gm@parity.fund]]></googleplay:owner><googleplay:email><![CDATA[gm@parity.fund]]></googleplay:email><googleplay:author><![CDATA[Parity]]></googleplay:author><itunes:block><![CDATA[Yes]]></itunes:block><item><title><![CDATA[History Ends Before the Singularity]]></title><description><![CDATA[Oracles from Inside the Horizon]]></description><link>https://newsletter.parity.fund/p/history-ends-before-the-singularity</link><guid isPermaLink="false">https://newsletter.parity.fund/p/history-ends-before-the-singularity</guid><dc:creator><![CDATA[KO-WEI TSENG]]></dc:creator><pubDate>Fri, 06 Nov 2026 10:03:44 GMT</pubDate><enclosure url="https://substack-post-media.s3.amazonaws.com/public/images/c2ec7e16-4295-4a72-8e1a-6721cbf13921_1600x900.png" length="0" type="image/jpeg"/><content:encoded><![CDATA[<div class="callout-block" data-callout="true"><p>This essay is by <strong>Kowei Tseng</strong> (X: <a href="https://x.com/kowei1995">@kowei1995</a>). He studied physics at National Taiwan University and earned a PhD in quantum physics at the Centre for Quantum Technologies, National University of Singapore, in 2023. He now leads IOTA&#8217;s ecosystem in Asia and writes about the singularity, privacy and quantum computing. His blog is <a href="https://physics2045.blog/">physics2045.blog</a>.</p><p>This essay was first published on the <a href="https://parity.fund/history-ends-before-the-singularity/">Parity website</a>; this newsletter edition is a reprint. There is also a <a href="https://parity.fund/zh/history-ends-before-the-singularity/">Chinese edition</a>. <a href="https://parity.fund/telescope-editions/">Telescope Editions</a> is Parity&#8217;s research grant program.</p></div><blockquote><p>&#8220;One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.&#8221;&#8212;Stanislaw Ulam, recalling a conversation with John von Neumann, 1958</p><p>&#8220;Thus the first ultraintelligent machine is the last invention that man need ever make.&#8221;&#8212;I. J. Good, 1965</p><p>&#8220;Within thirty years, we will have the technological means to create superhuman intelligence. Shortly after, the human era will be ended.&#8221;&#8212;Vernor Vinge, 1993</p></blockquote><div class="callout-block" data-callout="true"><p>I <a href="https://singularity-church.netlify.app/">read von Neumann, Good, Vinge, and Ray Kurzweil as prophets</a>: they wrote down prophecies, and we get to check the answers. I use the language of religion to talk about technology because it is the oldest and most complete grammar we have for facing something far beyond ourselves.</p></div><h2>Prologue: Seven Days Before Doomsday</h2><p>On November 4, 1960, <em>Science</em> published a paper whose title reads like a joke: &#8220;<a href="https://doi.org/10.1126/science.132.3436.1291">Doomsday: Friday, 13 November, A.D. 2026</a>.&#8221; The authors were the cybernetics pioneer Heinz von Foerster and two colleagues. They fit a curve to two thousand years of world population estimates and found it growing faster than an exponential: the doubling time itself kept shrinking. The curve is a hyperbola, and it goes to infinity in the year 2026.87.</p><p>As I write this, it is November 6, 2026, seven days before that Friday.</p><p>The hyperbola comes from growth feeding on itself: more people, more ideas; more ideas, more output; more output, more people fed. <a href="https://doi.org/10.2307/2118405">Michael Kremer modeled this mechanism in 1993</a>: for most of human history, the population growth rate was proportional to the population itself. An exponential only grows faster as it grows; a hyperbola grows disproportionately faster, and reaches infinity in finite time.</p><div class="callout-block" data-callout="true"><p>A growth rate proportional to the population means <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;dN/dt = aN^2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, which solves to <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;N(t) = 1/[a(t_0 - t)]&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and diverges at the finite time <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;t_0&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Exponential growth, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;dN/dt = aN&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, cannot reach infinity in finite time. Von Foerster&#8217;s fit was <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;N = K/(t_0 - t)^{0.99}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, almost exactly this ideal curve.</p></div><p>Population will not become infinite that day, of course. The world&#8217;s population growth rate peaked in the 1960s and has fallen ever since: as people grow better off, they tend to have fewer children, and the feedback loop breaks at the node called &#8220;people.&#8221;</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!zL0e!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!zL0e!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png 424w, https://substackcdn.com/image/fetch/$s_!zL0e!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png 848w, https://substackcdn.com/image/fetch/$s_!zL0e!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png 1272w, https://substackcdn.com/image/fetch/$s_!zL0e!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!zL0e!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png" width="1456" height="920" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:920,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Chart: world population from 1800 to 2023 against von Foerster's 1960 hyperbola. Until the mid-1990s the actual population roughly follows the curve; after that the curve shoots up and diverges on November 13, 2026, while the actual population grows almost linearly, about 8.1 billion in 2023 against 46.9 billion on the curve.&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Chart: world population from 1800 to 2023 against von Foerster's 1960 hyperbola. Until the mid-1990s the actual population roughly follows the curve; after that the curve shoots up and diverges on November 13, 2026, while the actual population grows almost linearly, about 8.1 billion in 2023 against 46.9 billion on the curve." title="Chart: world population from 1800 to 2023 against von Foerster's 1960 hyperbola. Until the mid-1990s the actual population roughly follows the curve; after that the curve shoots up and diverges on November 13, 2026, while the actual population grows almost linearly, about 8.1 billion in 2023 against 46.9 billion on the curve." srcset="https://substackcdn.com/image/fetch/$s_!zL0e!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png 424w, https://substackcdn.com/image/fetch/$s_!zL0e!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png 848w, https://substackcdn.com/image/fetch/$s_!zL0e!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png 1272w, https://substackcdn.com/image/fetch/$s_!zL0e!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F34d3970a-0af6-45fc-be17-cd17962243f2_1456x920.png 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Von Foerster&#8217;s doomsday curve against actual world population, 1800&#8211;2023. Data: <a href="https://ourworldindata.org/grapher/population">Our World in Data</a> (HYDE, Gapminder, UN WPP), <a href="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a></figcaption></figure></div><p>But the hyperbola is not quite dead. Producing intelligence takes GPUs, not wombs, and its cost is compute and electricity. Each smarter generation of models brings the next one sooner. Silicon has reconnected the loop that fertility broke. Seen this way, von Foerster did not miscalculate. He only bet on the wrong subject.</p><p>The singularity is not a date to wait for but a horizon. Humanity, I fear, has already fallen into the trapped region of the AGI singularity, where every outward path bends back inward. We are still some distance from the singularity itself, but we are already inside the horizon, and here every future leads to the same unavoidable end. Things will go on happening, but history will no longer have humanity as its subject.</p><h2>1. Confessions: A Singularitarian&#8217;s Ten-Year Posterior</h2><blockquote><p>The substrate was wrong. The law was right.</p></blockquote><p>I have believed in the singularity for more than ten years. &#8220;Believed&#8221; is not an exaggeration: my own blog is called <em>A Physics Apprentice Gazing at the Singularity</em> (&#20957;&#35222;&#22855;&#40670;&#30340;&#29289;&#29702;&#23416;&#24466;), its domain is physics2045, and that year comes from Kurzweil&#8217;s <em>The Singularity Is Near</em>. But I must confess: for most of those ten years, I was a believer in the framework and a heretic on the timeline.</p><p>I was a devout singularitarian as early as college. In 2016, with a recommendation letter from Ming-Shien Chang of Academia Sinica, I went to the Centre for Quantum Technologies (CQT) in Singapore to intern in an ion-trap lab. The same year, as a former president of the National Taiwan University Science Fiction Club, I <a href="https://www.youtube.com/watch?v=QL1brZl9vqg">gave a talk</a> at the Chinese Science Fiction Society (Taiwan), treating Kurzweil&#8217;s 2029 AGI as science fiction material, and at the club&#8217;s end-of-semester general meeting I screened his documentary <em>Transcendent Man</em> as a science fiction film. The lab and the club came in the same year, yet I treated them as two separate things: one was the reality of tuning lasers by hand, the other a distant future to tell stories about.</p><p>I later <a href="https://physics2045.blog/2020/09/27/cqt-interview-kowei/">stayed in that lab for a PhD</a>, storing quantum information in the vibrational states of Yb-171 ions (that is, phonons) to do quantum machine learning. The mainstream approach uses spin. Vibrational states are more fragile than spin, and though in theory they have infinitely many dimensions, in practice fewer than ten can be controlled. The work left me with an instinct: hardware is slow, and experiments sit far below their theoretical limits. In 2020, Singapore imposed its circuit breaker lockdown, and the lab was closed from late March to June, months in which the system had no air conditioning and lacked routine maintenance. After the restart, an alignment of a few tens of micrometers alone took weeks of repeated adjustment. Two high-power lasers failed at the same time: one was repaired, and the other defeated even the manufacturer&#8217;s engineers and was written off.</p><p>That is the instinct I brought to the singularity. Into the early 2020s, I still judged the framework right and the timeline wildly overoptimistic. I could even point to where Kurzweil was wrong: the nanobots he bet on were far behind, and none of his three GNR tracks (genetics, nanotechnology, robotics) was on his schedule. When ChatGPT arrived in 2022, I did not take it as the template for AGI. When I read <em>The Singularity Is Nearer</em> in 2024, what worried me was his unbelievably optimistic Whig view of history, and I <a href="https://physics2045.blog/2024/07/30/singularity-is-nearer/">wrote</a> that if biological enhancement won out over mind uploading, the singularity would slip by at least a decade: &#8220;a Type I civilization could be delayed to the end of the twenty-first century.&#8221;</p><p>Fast-forward to 2026, and Kurzweil&#8217;s singularity year of 2045 has become the conservative timeline. He bet that a machine would pass the Turing test by 2029. In March 2025, a paper on a preregistered three-party Turing test went up on <a href="https://arxiv.org/abs/2503.23674">arXiv</a>, reporting that GPT-4.5, prompted to play a human, was judged to be the human 73% of the time, more often than the real humans in the same sessions. The milestone was met four years early. This May, in a <a href="https://physics2045.blog/2026/05/22/iota-restructure-stop-worrying-love-ai/">diary post</a>, I borrowed the subtitle of <em>Dr. Strangelove</em> and wrote &#8220;How I Learned to Stop Worrying and Love AI&#8221;: within a few months I had gone from fearing replacement to running several agents at once, every day.</p><p>In 2020 I wrote on my blog about a story Kurzweil tells: seven years into the Human Genome Project, 1% was done, and frontline scientists estimated seven hundred more years. Kurzweil said that on an exponential, it was already half finished. At the time I took it as just a pretty parable. Then this October I went through the large batch of proofs OpenAI released all at once, in both mathematics and computer science, and not one of them was about cryptography. In 1942, noticing that fission papers had vanished from the journals, the Soviet physicist Georgy Flerov <a href="https://www.nybooks.com/articles/1995/02/16/the-communist-bomb/">inferred that the United States was secretly building an atomic bomb</a>. Cryptography rests on the bet that &#8220;some problems are just hard.&#8221; OpenAI&#8217;s silence on cryptography made me feel that this bet may be growing shaky, and that I might be one of the people in the story looking at 1% and saying seven hundred years.</p><p>In Bayesian terms, my prior was wrong because of a linear intuition, and every &#8220;surprise&#8221; was the same signal replaying. The intuition came from that written-off laser and those weeks of micrometer alignment. I used the slowness of hardware to estimate an exponential curve in software, so no wonder I once believed ECDSA would hold until 2035. The nanobots have not come, but the law of accelerating returns has not missed a single day in the domain of information. The singularity may be born of matrix multiplication.</p><h2>2. On Eras: The Year History Starts Over</h2><blockquote><p>In a Chaotic Era, the calendar is the first to die.</p></blockquote><p>Every civilization needs a year one, and the great dystopias have quietly changed the calendar too.</p><p>In <em>The Matrix</em>, the machines keep humanity living forever in 1999, which Agent Smith calls &#8220;the peak of your civilization.&#8221; Aldous Huxley&#8217;s <em>Brave New World</em> restarts history in 1908, the year the Model T appeared, and dates its years A.F., After Ford. The cross, with its top cut off, became a T.</p><p>Real history has done the same. In the autumn of 1793, the French National Convention adopted the <a href="https://archives.senat.fr/pdf/Pixerecourt/FR_SENAT_3FPX001.102_1775.pdf">Republican Calendar</a> and set the first day of year one on the first day of the Republic: September 22, 1792. The twelve months were renamed after the weather and farm work around Paris, among them Brumaire, Frimaire, Thermidor, and Fructidor; the week became ten days, the rest day moved from Sunday to the tenth day, and for a time the day was to have ten hours. By the time the new calendar passed, year one was already over. It was recognized in hindsight. The calendar lasted twelve years. Napoleon abolished it after proclaiming himself emperor, and the old calendar returned on January 1, 1806.</p><p>I used to think our generation&#8217;s year one was 2008: the year of the financial crisis and of Satoshi Nakamoto&#8217;s Bitcoin white paper. Bitcoin&#8217;s genesis block even carries its own declaration of an era: on January 3, 2009, that day&#8217;s <em>Times</em> headline on a second bank bailout was engraved into it. That was the era of money.</p><p>But if I may recognize it in hindsight, as the National Convention did, I would set the first day of year one on November 30, 2022, the day ChatGPT went live.</p><p>In Liu Cixin&#8217;s Three-Body world, the motion of the three suns has no closed-form solution, calendars fail, and civilization can only dehydrate and wait. A Chaotic Era is terrifying because the predictability horizon shrinks below the planning cycle.</p><p>The &#8220;unpredictability&#8221; of a Chaotic Era is in fact a quantity you can compute. In a chaotic system, two trajectories that start a hair apart separate exponentially with time: with every Lyapunov time, the error grows by a factor of about 2.7. Improve the measurement precision tenfold, and the forecast gains only about 2.3 Lyapunov times. The Lyapunov time of weather is measured in days, so no number of satellites will push forecasts much past two weeks. The Lyapunov time of the inner planets is about five million years, which is why astronomers can compute their orbits tens of millions of years ahead.</p><p>The advance of civilization has a Lyapunov time of its own. The best yardstick is METR&#8217;s <a href="https://metr.org/blog/2025-03-19-measuring-ai-ability-to-complete-long-tasks/">measurement</a> in 2025: the length of task an AI can complete on its own, measured by the time a human expert would need, doubles roughly every seven months. A five-year plan spans about 8.6 doublings. By the time the plan ends, the capability it relied on is more than three hundred times what it was when the plan was drafted. Worse, the doubling time itself is uncertain: mistake seven months for ten, and after five years you are off by nearly a factor of six. A plan&#8217;s assumptions rarely outlast the plan.</p><div class="callout-block" data-callout="true"><p>Let the initial error be <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\delta_0&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, the tolerable error <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\Delta&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and the largest Lyapunov exponent <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\lambda&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. The error grows as <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\delta_0 e^{\\lambda t}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, so the predictable time is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;T = \\ln(\\Delta/\\delta_0)/\\lambda&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and the Lyapunov time is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;1/\\lambda&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. A tenfold gain in precision adds only <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\ln 10/\\lambda \\approx 2.3/\\lambda&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> to <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;T&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. The task-length arithmetic: 60 months <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\div&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> 7 months <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\approx&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> 8.6 doublings, and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^{8.6} \\approx 390&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>; if the doubling time is misjudged as ten months, five years count only 6 doublings, a factor of 64, and the two differ by a factor of about 6.</p></div><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!1Ejy!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!1Ejy!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp 424w, https://substackcdn.com/image/fetch/$s_!1Ejy!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp 848w, https://substackcdn.com/image/fetch/$s_!1Ejy!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp 1272w, https://substackcdn.com/image/fetch/$s_!1Ejy!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!1Ejy!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp" width="1456" height="800" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/fd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:800,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;METR&#8217;s chart: AI models released from 2019 to 2025, with the length of task they complete at 50% reliability (in human time, log scale) rising from a few seconds for GPT-2 to over an hour for o3, along a straight line with a doubling time of about 207 days&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="METR&#8217;s chart: AI models released from 2019 to 2025, with the length of task they complete at 50% reliability (in human time, log scale) rising from a few seconds for GPT-2 to over an hour for o3, along a straight line with a doubling time of about 207 days" title="METR&#8217;s chart: AI models released from 2019 to 2025, with the length of task they complete at 50% reliability (in human time, log scale) rising from a few seconds for GPT-2 to over an hour for o3, along a straight line with a doubling time of about 207 days" srcset="https://substackcdn.com/image/fetch/$s_!1Ejy!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp 424w, https://substackcdn.com/image/fetch/$s_!1Ejy!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp 848w, https://substackcdn.com/image/fetch/$s_!1Ejy!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp 1272w, https://substackcdn.com/image/fetch/$s_!1Ejy!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd22115a-e7ca-4a87-b7eb-4b2d56554ce1_1628x894.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Length of tasks AI agents can complete, 2019&#8211;2025. Chart: <a href="https://arxiv.org/abs/2503.14499">Kwa et al. 2025</a> (METR), <a href="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a></figcaption></figure></div><p>Strangely, while five-year plans fail, prophecies from thirty years ago have held up rather well. Chaos theory has an account of this too: weather cannot be forecast past two weeks, yet climate can be discussed a century out, because individual trajectories diverge while the region they end up in, the attractor, keeps a stable shape. What prophets see is the attractor. The Third Prophet, Vinge, wrote &#8220;within thirty years&#8221; in 1993. Thirty years later is 2023, and ChatGPT went live at the end of 2022. He died on March 20, 2024, just in time to see the curve begin to bend upward. Strictly speaking, ChatGPT is not the superhuman intelligence he meant, and to count it as fulfillment is the way of chenwei, the old Chinese lore of reading omens as prophecy. Let it stand as a coincidence.</p><p>Elon Musk wrote in 2014: &#8220;Hope we&#8217;re not just the biological boot loader for digital superintelligence. Unfortunately, that is increasingly probable.&#8221; John the Baptist stated the fate of a boot loader long ago: he must increase, but I must decrease. It is the first to wake in the dark, loads the real operating system into memory, hands over control, and then never runs again.</p><h2>3. On Scale: Ten Thousand Years, a Hundred Years, Ten Weeks</h2><blockquote><p>Ten thousand years is an instant, a hundred years is long, and ten weeks is thirty years.</p></blockquote><p>On Carl Sagan&#8217;s Cosmic Calendar, which compresses the universe&#8217;s 13.8 billion years into a single year, one second is about 437 years. The twelve thousand years of the agricultural era are the last 27 seconds of New Year&#8217;s Eve; from the Trinity test in 1945 to 2045 is 0.23 seconds; from ChatGPT&#8217;s launch to today is 9 milliseconds.</p><p>From 1945 to 2045 is exactly a hundred years, and the same man joins the two ends: the First Prophet, von Neumann, worked on the implosion design of the atomic bomb and is the first person on record to speak of a &#8220;singularity.&#8221;</p><p>The economist Robin Hanson <a href="https://mason.gmu.edu/~rhanson/longgrow.pdf">fit two million years of world product to a sequence of exponential growth modes</a>:</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!cQpK!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!cQpK!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png 424w, https://substackcdn.com/image/fetch/$s_!cQpK!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png 848w, https://substackcdn.com/image/fetch/$s_!cQpK!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png 1272w, https://substackcdn.com/image/fetch/$s_!cQpK!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!cQpK!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png" width="1368" height="644" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/e1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:644,&quot;width&quot;:1368,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;&#34920;&#26684; 1&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="&#34920;&#26684; 1" title="&#34920;&#26684; 1" srcset="https://substackcdn.com/image/fetch/$s_!cQpK!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png 424w, https://substackcdn.com/image/fetch/$s_!cQpK!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png 848w, https://substackcdn.com/image/fetch/$s_!cQpK!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png 1272w, https://substackcdn.com/image/fetch/$s_!cQpK!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1c67c66-a4d3-402d-923a-1116d356133d_1368x644.png 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>In a world that doubles every two weeks, growing 32-fold takes 5 doublings, that is, ten weeks; the same growth took the industrial era 31.5 years.</p><p>The next mode will come because intelligence is itself the function that produces technology: fire, writing, the steam engine, electricity, the internet are all its products. The Second Prophet, Good, put it more directly: it will be the last invention.</p><p>Kremer&#8217;s loop in the prologue accelerates itself because population can accumulate: output feeds more people, more people think of more ideas, and ideas turn into more output. In the standard growth model, machines and factories can be accumulated through investment, but labor can only wait for the population to grow; so once humans got rich and chose to have fewer children, the loop broke at the node of labor, and growth fell back from hyperbolic to exponential. With AI, labor too can be bought with investment. Output can be turned into chips, and chips can run more agents. If enough work can be automated, the same model&#8217;s conclusion flips from diminishing returns to increasing returns, and the growth rate itself begins to rise.</p><div class="callout-block" data-callout="true"><p>In the Cobb&#8211;Douglas production function <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Y = AK^{\\alpha}L^{1-\\alpha}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, only capital <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;K&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> can be accumulated through investment, and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\alpha < 1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> gives it diminishing returns, so growth eventually slows to the pace of population and technology. If AI lets labor <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;L&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> be bought with capital too, output has constant returns to the accumulable inputs; hand the research that sets the technology level <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> to AI as well, and the total returns to accumulable inputs exceed one. The growth rate then rises with the size of the economy, and the hyperbola of the prologue, diverging in finite time, can reappear.</p></div><p>This curve has left traces in the data. In 2020, David Roodman of Open Philanthropy fit <a href="https://coefficientgiving.org/research/modeling-the-human-trajectory/">world product since 10,000 BCE</a> to a superexponential curve with random shocks, and its median explosion lands in 2047, two years from Kurzweil&#8217;s 2045. He does not himself believe the economy will actually reach infinity, because he sees the system called &#8220;humanity&#8221; as inherently unstable. The growth of the past thirty years has also kept to the low side of his model&#8217;s prediction, and I think the reason is the loop that broke at the link called &#8220;people.&#8221;</p><p>The case against this also comes from growth theory. In 2023, Ege Erdil and Tamay Besiroglu <a href="https://arxiv.org/abs/2309.11690">went through nine objections</a> to explosive growth one by one, among them regulation, production bottlenecks, alignment, and the speed of automation. They judged most of them inconclusive, but four questions remain open: how strongly regulation will respond, what physical bottlenecks production has, how much superhuman capability is worth economically, and how fast automation can be completed. The economist William Baumol saw another layer in the 1960s: sectors whose productivity improves fastest make ever cheaper products and so shrink as a share of the economy, and total growth is to some degree set by the slowest sector. If even one necessary link is stuck on people or on physical limits, the doubling time is held back.</p><p>That returns will flip from diminishing to increasing is the largest assumption in this essay, and the data do not yet support it. <a href="https://doi.org/10.1257/aer.20180338">Nicholas Bloom and colleagues</a> found that the ideas produced per American researcher halve about every thirteen years. AI can copy researchers, but it first has to outrun that decay. Goldman Sachs also <a href="https://www.techtimes.com/articles/328112/20260928/goldman-sachs-quantifies-ais-230b-annual-gap-800b-spent-300b-needed-break-even.htm">estimates</a> that the five largest American cloud providers will spend about $800 billion on AI this year, that breaking even would take $300 billion a year in AI revenue, and that through the second quarter of this year the extra cloud revenue from AI was only about $70 billion, a shortfall of $230 billion.</p><h2>4. On the Horizon: Why History Has Ended</h2><blockquote><p>At the moment you cross the horizon, nothing happens. That is what makes the horizon terrifying.</p></blockquote><p>Using a black hole as a metaphor for the singularity is nothing new. <a href="https://www.writingsbyraykurzweil.com/?p=80931">Responding</a> to Kevin Kelly&#8217;s critique in 2006, Kurzweil explained that what he borrowed was the event horizon surrounding a black hole, the boundary that is hard to see past from outside. The point of infinite density at the center is not part of his metaphor. <a href="https://kk.org/thetechnium/the-singularity/">Kelly&#8217;s critique</a> was aimed at the curve: on a log-log plot, whichever year you stand in, an exponential looks like it is heading for the vertical, so the singularity is always &#8220;near.&#8221;</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!iCY7!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!iCY7!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp 424w, https://substackcdn.com/image/fetch/$s_!iCY7!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp 848w, https://substackcdn.com/image/fetch/$s_!iCY7!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp 1272w, https://substackcdn.com/image/fetch/$s_!iCY7!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!iCY7!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp" width="1177" height="904" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:904,&quot;width&quot;:1177,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Kurzweil&#8217;s &#8220;Countdown to Singularity&#8221; log plot: from the origin of life, the Cambrian explosion, upright-walking human ancestors, agriculture, printing, the Industrial Revolution to the personal computer, the interval from each event to the next shrinks with the years before the present, lining up on a straight line&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Kurzweil&#8217;s &#8220;Countdown to Singularity&#8221; log plot: from the origin of life, the Cambrian explosion, upright-walking human ancestors, agriculture, printing, the Industrial Revolution to the personal computer, the interval from each event to the next shrinks with the years before the present, lining up on a straight line" title="Kurzweil&#8217;s &#8220;Countdown to Singularity&#8221; log plot: from the origin of life, the Cambrian explosion, upright-walking human ancestors, agriculture, printing, the Industrial Revolution to the personal computer, the interval from each event to the next shrinks with the years before the present, lining up on a straight line" srcset="https://substackcdn.com/image/fetch/$s_!iCY7!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp 424w, https://substackcdn.com/image/fetch/$s_!iCY7!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp 848w, https://substackcdn.com/image/fetch/$s_!iCY7!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp 1272w, https://substackcdn.com/image/fetch/$s_!iCY7!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F388c39f2-796c-4377-ace8-20dbf162b703_1177x904.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Kurzweil&#8217;s &#8220;Countdown to Singularity.&#8221; Image: Ray Kurzweil, Kurzweil Technologies, Inc., <a href="https://commons.wikimedia.org/wiki/File:PPTCountdowntoSingularityLog.jpg">Wikimedia Commons</a>, <a href="https://creativecommons.org/licenses/by/1.0/">CC BY 1.0</a></figcaption></figure></div><p>The critique is usually quoted up to this point, but Kelly&#8217;s argument had a second half. He held that such a turning point cannot be noticed from inside at all, only recognized afterward. In &#8220;<a href="https://kk.org/thetechnium/thinkism/">Thinkism</a>&#8221; in 2008 he wrote: &#8220;Then one day in the future, we&#8217;ll realize it already happened.&#8221; This February, twenty years after the critique was written, he <a href="https://kevinkelly.substack.com/p/the-singularity-is-always-near">reposted</a> the old piece with a new line in front: &#8220;It will always appear as if it is about to happen, even if the shift point has already past.&#8221;</p><p>The two seem opposed, but they share a premise: <strong>the observer stands outside the horizon, and the horizon is a wall that cannot be seen through.</strong> In physics, though, the event horizon is defined by the impossibility of getting out. Someone who has crossed it still sees the starlight outside. What they have lost is the possibility of returning and sending a signal out. Kurzweil speaks of those outside not seeing in. I want to stress that those inside cannot get out, and that we may already be inside. So Kelly is my ally: if the horizon can only be identified afterward, then &#8220;not yet crossed&#8221; and &#8220;crossed long ago&#8221; look exactly the same from inside.</p><p>Let us push the metaphor into the physics and see where it holds and where it breaks.</p><p>A black hole captures matter in layers. At <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;6GM/c^2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> from the center lies the innermost stable circular orbit: outside it, matter can still orbit stably; past it, there are no stable orbits left, only the spiral inward. If our age has such a boundary, it may be 2012: AlexNet turned deep learning around overnight, and since then capital, talent, and compute have found no stable orbit that circles AI without falling in.</p><p>Matter shines as it falls into a black hole. The brightest persistent objects in the universe are quasars, lit by matter falling in: an accretion disk converts about 6% (for a non-rotating black hole) to 42% (for one spinning at the limit) of rest mass into radiation, eight to sixty times the efficiency of hydrogen fusion. The capital spending, valuations, and breakthroughs of our age may be like the light of the accretion disk, the last brilliance humanity gives off before being swallowed.</p><p>Then the horizon itself. If the black hole is large enough, a traveler crossing the event horizon feels nothing, and the equivalence principle guarantees it: local physics goes on as usual, with no alarm and no tearing. The larger the hole, the gentler the entrance. If we really did cross a horizon, it was most likely in 2022. That October, the United States imposed export controls on advanced chips to China, and compute formally became a stake in geopolitics. Less than two months later, on November 30, ChatGPT went live. That day, as on any ordinary day in history, the world showed nothing unusual.</p><p>But there is no escaping the word &#8220;if.&#8221; Whether a region lies inside an event horizon depends on whether the light it emits can eventually escape to infinity, and that is known only at the end of time. That is why physicists say the event horizon can only be <a href="https://arxiv.org/abs/gr-qc/0508107">teleological</a>: it is determined by the entire future of spacetime, and it can even appear first in a patch of flat, unremarkable spacetime, merely because a black hole will form there later. If &#8220;already crossed&#8221; rests on the event horizon alone, it can never be tested, and it is no different from an omen.</p><p>General relativity has another criterion, one that can be checked locally and in the present: the trapped surface. On an ordinary sphere, light sent outward spreads out; on a trapped surface, even the outward light converges, and every direction leads inward. Enclose all the trapped surfaces at one moment, and the outermost boundary is the apparent horizon. It differs from the event horizon: (a) it can be identified from present information alone; (b) it changes and can expand, shrink, or even disappear.</p><p>Roger Penrose <a href="https://doi.org/10.1103/PhysRevLett.14.57">proved in 1965</a> that once a trapped surface appears, given an energy condition (roughly, that gravity is always attractive) and a reasonable causal structure, spacetime must contain a light ray that stops dead after a finite distance and cannot be extended. In a black hole, that means hitting the singularity. The proof won him the Nobel Prize in Physics in 2020.</p><div class="callout-block" data-callout="true"><p>A trapped surface is a closed two-dimensional surface from which both families of light rays sent out perpendicular to it, inward and outward, converge toward the future. The apparent horizon is the outermost marginally trapped surface on a given time slice, where the outward light neither spreads nor converges; slice spacetime differently, and its position moves. If the cosmic censorship conjecture holds, a trapped surface must lie inside some black hole (Hawking &amp; Ellis 1973). The precise statement of Penrose&#8217;s theorem: if a spacetime has a non-compact Cauchy surface, satisfies the null energy condition, and contains a closed trapped surface, then it is future null geodesically incomplete. The theorem guarantees only incompleteness; &#8220;hitting the singularity&#8221; is the physical reading.</p></div><p>At the scale of civilization, two observable conditions can replace the vague metaphor of &#8220;crossing the horizon.&#8221;</p><ul><li><p>The trapping condition: every outward option of the major actors, including pausing, exiting, and banning, ends up as deeper investment; no party can exit unilaterally without being eliminated.</p></li><li><p>The energy condition: the returns on investment in intelligence stay positive and feed back into the production of intelligence itself (the increasing returns of chapter 3).</p></li></ul><p>When both hold, as when a trapped surface meets an energy condition, the end cannot be avoided; if either fails, the claim of this essay fails with it.</p><p>The trapping condition took shape around 2022, and the evidence since has pointed one way. In March 2023, <a href="https://futureoflife.org/open-letter/pause-giant-ai-experiments/">an open letter</a> called on all labs to pause training of systems stronger than GPT-4 for at least six months. Not one frontier lab actually stopped, and Musk, among the letter&#8217;s best-known signatories, announced xAI four months later. Even as chip controls try to slow a rival, open-weight models spread generation after generation, blunting any one country&#8217;s unilateral ban. Outward thrust ends up as inward velocity.</p><p>If a lab really did stop and was still at the frontier two years later, if nations signed a compute treaty with inspectors, or if the <a href="https://epoch.ai/blog/training-compute-of-frontier-ai-models-grows-by-4-to-5x-per-year">compute</a> used by frontier models fell two years in a row, then my premise would be wrong. So far none of this has happened.</p><p>As I see it, the trapped surface has appeared. Whether an event horizon has really formed depends on the future, and can only be left to the kind of hindsight Kelly describes. An apparent horizon can shrink, and it can disappear. Until it does, assume we really are inside.</p><p>Inside the horizon, though, two things have changed.</p><p><strong>First, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\pmb{r}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> has turned from space into time.</strong> Inside the Schwarzschild geometry, the radial coordinate becomes timelike: every future light cone tips inward, and the singularity <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;r = 0&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> becomes a moment in time, like tomorrow, with no way around it. Inside the horizon, &#8220;outside&#8221; is no longer a direction. This is what &#8220;the end of history&#8221; means: things still happen every day, but every future worldline ends in the same place.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!A5D5!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!A5D5!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png 424w, https://substackcdn.com/image/fetch/$s_!A5D5!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png 848w, https://substackcdn.com/image/fetch/$s_!A5D5!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png 1272w, https://substackcdn.com/image/fetch/$s_!A5D5!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!A5D5!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png" width="1456" height="1456" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/a126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1456,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Schematic: as a star collapses into a black hole, the light cones tip further inward the closer they are to the center; past the event horizon, every future direction points to the singularity.&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Schematic: as a star collapses into a black hole, the light cones tip further inward the closer they are to the center; past the event horizon, every future direction points to the singularity." title="Schematic: as a star collapses into a black hole, the light cones tip further inward the closer they are to the center; past the event horizon, every future direction points to the singularity." srcset="https://substackcdn.com/image/fetch/$s_!A5D5!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png 424w, https://substackcdn.com/image/fetch/$s_!A5D5!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png 848w, https://substackcdn.com/image/fetch/$s_!A5D5!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png 1272w, https://substackcdn.com/image/fetch/$s_!A5D5!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa126caf9-89f5-4eed-8a3e-92eccc63684f_1456x1456.png 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Light cones around a collapsing star. Image: adapted from Cmglee (after Penrose), <a href="https://commons.wikimedia.org/wiki/File:Light_cones_near_black_hole.svg">Wikimedia Commons</a>, <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a></figcaption></figure></div><p><strong>Second, the remaining proper time has a maximum.</strong> From the horizon to the singularity, the longest proper time is</p><p>It is reached on one particular free-fall path: start from rest at the horizon, do nothing, and let the geometry carry you. This is the twin paradox in its general-relativistic form: <strong>of two worldlines, the one that does not accelerate ages more.</strong> Inside the horizon, any thrust, inward or outward, takes you off this longest path. <a href="https://arxiv.org/abs/0705.1029">Geraint Lewis and Juliana Kwan worked out the details in 2007</a>: if you crossed the horizon already carrying velocity, a burn of just the right size can bring you back near that path, and the time left grows, but it never exceeds the maximum. In other words, the most intuitive struggle, pushing outward with all you have, only brings the end sooner.</p><div class="callout-block" data-callout="true"><p>Proper time is the time measured by the clock you carry, that is, the time you actually experience. Take <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;G = c = 1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Inside a Schwarzschild black hole, the proper time of radial motion satisfies</p><p>Inside the horizon <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;t&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is a spatial coordinate, and the second term always subtracts: any motion in the <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;t&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> direction is deducted from proper time. So the worldline with <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;dt = 0&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is the longest, and integrating gives</p><p>which in ordinary units is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\pi GM/c^3&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. This worldline is exactly the geodesic with energy <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;E = 0&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, the one that falls from rest at the horizon. Anyone already on it who fires in either radial direction gains velocity in the <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;t&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> direction, and the time only shortens.</p></div><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!GOjC!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!GOjC!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png 424w, https://substackcdn.com/image/fetch/$s_!GOjC!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png 848w, https://substackcdn.com/image/fetch/$s_!GOjC!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png 1272w, https://substackcdn.com/image/fetch/$s_!GOjC!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!GOjC!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png" width="1456" height="803" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:803,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Line chart: after crossing the horizon, firing a rocket at constant thrust, the remaining proper time as a percentage of the maximum. The horizontal axis is the thrust, inward on the left, outward on the right, free fall in the middle. Someone who fell from rest at the horizon reaches the maximum exactly in free fall and loses time by thrusting either way; someone who fell in with velocity from afar has about 42% in free fall, peaks at about 57% with a little outward thrust, loses time by thrusting harder, and never reaches the maximum.&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Line chart: after crossing the horizon, firing a rocket at constant thrust, the remaining proper time as a percentage of the maximum. The horizontal axis is the thrust, inward on the left, outward on the right, free fall in the middle. Someone who fell from rest at the horizon reaches the maximum exactly in free fall and loses time by thrusting either way; someone who fell in with velocity from afar has about 42% in free fall, peaks at about 57% with a little outward thrust, loses time by thrusting harder, and never reaches the maximum." title="Line chart: after crossing the horizon, firing a rocket at constant thrust, the remaining proper time as a percentage of the maximum. The horizontal axis is the thrust, inward on the left, outward on the right, free fall in the middle. Someone who fell from rest at the horizon reaches the maximum exactly in free fall and loses time by thrusting either way; someone who fell in with velocity from afar has about 42% in free fall, peaks at about 57% with a little outward thrust, loses time by thrusting harder, and never reaches the maximum." srcset="https://substackcdn.com/image/fetch/$s_!GOjC!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png 424w, https://substackcdn.com/image/fetch/$s_!GOjC!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png 848w, https://substackcdn.com/image/fetch/$s_!GOjC!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png 1272w, https://substackcdn.com/image/fetch/$s_!GOjC!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F01c773ac-ba10-40c2-acf4-9cf7eded3529_1456x803.png 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Remaining proper time under constant thrust inside the horizon. Computed after <a href="https://arxiv.org/abs/0705.1029">Lewis &amp; Kwan 2007</a></figcaption></figure></div><p>Read through this metaphor, then, the Fourth Prophet Kurzweil&#8217;s 2045 is not a prediction but a maximum. The &#8220;conservative timeline&#8221; is the longest lifetime the quietest geodesic can give. His 2045 was only extrapolated from the compute curve, not computed from <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\tau_{\\max}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> (a civilization has no measurable mass, of course). That arms races and accelerationism shorten this timeline is intuitive. What is counterintuitive is that a deliberate struggle to escape brings the end sooner too.</p><p>In this essay, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\tau&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is the time left for alignment research, institutions, and human adaptation before the end. The end means the moment humanity ceases to be the subject of history. Whether it is coming of age, being replaced, or making a covenant with a second subject, it happens only once, and the outcome depends on how much we prepare beforehand. So the longer <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\tau&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, the better.</p><p>Putting this together yields the least welcome proposition in this essay: inside the horizon, pauses, bans, and unilateral exits, as long as they are only thrust and do not change the geometry itself, likewise only shorten the time that remains.</p><p>Why &#8220;only thrust&#8221;? Some examples:</p><ol><li><p><strong>Compute overhang.</strong> A pause can only stop training. During the pause, chips and compute still get cheaper, and frontier research still goes on. By <a href="https://epoch.ai/publications/algorithmic-progress-in-language-models">Epoch AI&#8217;s estimate</a>, the compute a language model needs to reach a given level of performance halves about every eight months. At that rate, when a six-month pause ends, algorithmic progress alone gives the same budget about 70% more effective compute, before counting better chips. The accumulated gap is released all at once when training resumes, and the curve folds into a steeper step.</p></li><li><p><strong>Selection effect.</strong> A unilateral pause hands the frontier to whoever is least willing to pause. Those willing to stop tend to be the ones who care most about risk. Once they stop, the lead flows to the least careful actors. The open letter above has already demonstrated this once.</p></li><li><p><strong>Going dark.</strong> A ban moves research somewhere else, usually into the military, offshore, or out of public view: less transparency, a fiercer race. Biological weapons are the precedent. The Soviet Union signed the Biological Weapons Convention in 1972, soon founded Biopreparat under civilian cover, and over the following two decades built the largest secret biological weapons program in the world, with staff in the tens of thousands.</p></li><li><p><strong>Proliferation.</strong> The more tightly the frontier is restricted, the more capability flows into open weights, and weights, once published, cannot be recalled. Chip controls were meant to slow a rival. In January 2025, DeepSeek, itself under those controls, released the <a href="https://huggingface.co/deepseek-ai/DeepSeek-R1">reasoning model R1</a> under an MIT license, claimed parity with OpenAI&#8217;s o1, and let anyone download, modify, and redistribute it. Any future attempt to control intelligence has to start from the versions already out.</p></li></ol><div class="callout-block" data-callout="true"><p>The 95% confidence interval of <a href="https://epoch.ai/publications/algorithmic-progress-in-language-models">Epoch AI&#8217;s estimate</a> is 5 to 14 months; &#8220;70%&#8221; is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^{6/8} - 1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. For the scale of the Soviet program, see Leitenberg, Zilinskas, and Kuhn, <em><a href="https://doi.org/10.4159/harvard.9780674065260">The Soviet Biological Weapons Program: A History</a></em> (2012).</p></div><p>All four mechanisms change only the thrust. The geometry itself is unchanged. The geometry here is the winner-take-all payoff structure of the intelligence game. As long as the structure stands, unilateral thrust only changes lanes in the same funnel.</p><p>A pause looks like the &#8220;just right&#8221; burn of Lewis and Kwan, but the examples make it plain: it does not cancel the excess velocity; it only stores it and hands it to someone else. And &#8220;just right&#8221; exists only in theory. To compute that burn you must know the mass of the black hole, the thrust of your engine, your velocity at the horizon, and exactly how long to fire. Any error turns the correction into the struggle that drags someone deeper into a swamp. A civilization cannot measure its mass or its velocity, and no one can flip the switch for all actors at once.</p><p>We have to look for the exit in the premises of Penrose&#8217;s theorem. The theorem says that with a trapped surface, an energy condition, and a causal structure all present, the end cannot be avoided. Read in reverse, it says that removing any one premise opens a possible way out (a change in the geometry itself):</p><ul><li><p>The trapped surface disappears: a major actor appears that can credibly exit without being eliminated for it.</p></li><li><p>The energy condition breaks: the feedback loop snaps at data, energy, cooling, or the cost of verification. Values, taste, and politics&#8212;the domains without cheap verifiers&#8212;may be the last stronghold of human agency.</p></li><li><p>The causal structure is rewritten: treaties, institutions, and technical choices change the game directly.</p></li></ul><p>A test particle can only move along a given geometry. Its mass is too small to change spacetime. A civilization is different. In Einstein&#8217;s equations, what curves spacetime is matter and energy, and a civilization is the mass-energy of this game. The traveler in the black hole has only a rocket. A civilization rewrites the right-hand side of the equation.</p><p>History has precedents. The nuclear arms race of the Cold War was almost the same game: whoever stopped developing first handed their security to the other side. Warheads worldwide <a href="https://journals.sagepub.com/doi/10.2968/056002019">peaked at about seventy thousand in 1986</a> and have fallen since to around twelve thousand today. The <a href="https://www.armscontrol.org/factsheets/inftreaty">INF Treaty</a> of 1987 marked the first time two superpowers destroyed an entire class of missile, 2,692 in all, and it rested on each side sending inspectors to verify at the other&#8217;s bases. Civilian nuclear power has been stopped too: Austria <a href="https://noe.gv.at/noe/Umweltschutz/40JahreVolksabstimmung_Teil1.html">rejected by referendum</a> in 1978 the finished Zwentendorf plant, which never ran a day. Italy, after Chernobyl and a <a href="https://dait.interno.gov.it/documenti/referendum_risultati_complessivi_1946_2016_0.pdf">1987 referendum</a>, had shut down all its nuclear plants by 1990. Our civilization has exited a technological path before.</p><p>Why is AI different? The geometry of nuclear power could be bent because:</p><ol><li><p>Nuclear weapons have simple, verifiable bottlenecks: enriched uranium and plutonium need enormous facilities, test explosions are recorded by seismographs, and a treaty can send people to count missiles on site. AI weights are just a string of bits that can be copied. Only the chips that train them can be seen and counted.</p></li><li><p>The returns on nuclear weapons have a ceiling: once there are enough warheads to destroy the other side, the marginal gain in force approaches zero. A country that gives up nuclear power still has coal and gas. The returns on AI, by contrast, feed back into its own production: the energy condition above.</p></li></ol><div class="callout-block" data-callout="true"><p>The figures follow the estimates of the Federation of American Scientists (FAS) and the <em>Bulletin of the Atomic Scientists</em>: a 1986 peak of about seventy thousand, including retired warheads awaiting dismantlement; about twelve thousand in early 2026. Chips make a lever for governance because compute is visible, blockable, and countable, and its supply chain is extremely concentrated.</p></div><p>So if there is a way out, it most likely runs through chips: a treaty with verification, plus <a href="https://arxiv.org/abs/2402.08797">compute governance at the chip level</a>. A treaty cannot by itself change the trend, though. Nuclear treaties can destroy existing missiles but cannot guarantee that the research stops. Likewise, even if an AI treaty could control the chips, algorithms would still improve, and when training resumed, the step toward the singularity would still be there. In the best case, thrust can at most pull the time back toward the theoretical maximum. Only geometry can change the maximum itself.</p><h2>5. On Invasion: From Symbols to Atoms</h2><blockquote><p>Machines first conquer the world that can be verified, then remake the world so that it can be.</p></blockquote><p>On May 20, 2026, a general-purpose reasoning model <a href="https://openai.com/index/model-disproves-discrete-geometry-conjecture/">disproved on its own</a> the planar unit distance conjecture that Paul Erd&#337;s posed in 1946. Timothy Gowers, in the <a href="https://arxiv.org/abs/2605.20695">explanatory paper</a> published alongside the proof, called it a milestone for AI mathematics.</p><p>Five months later, the crack opened. On October 25, 2026, OpenAI released a <a href="https://github.com/openai/math/blob/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/paper.pdf">preprint</a> titled &#8220;The Exponential Time Hypothesis Is False,&#8221; with a formal proof in Lean: its internal model had produced a deterministic algorithm that counts the solutions of a k-CNF formula in polynomial space and about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^{O(n \\log\\log n/\\sqrt{\\log n})}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> time. The saving in the exponent is only a factor of about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\sqrt{\\log n}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and the running time is still astronomical, but that is enough to refute the Exponential Time Hypothesis (ETH) that Russell Impagliazzo and Ramamohan Paturi proposed in 1999 (that 3-SAT has no subexponential algorithm). A cornerstone of a generation of complexity theory has cracked. Hours later, Anthropic published <a href="https://github.com/anthropics/formal-math/blob/16a5ce41304fcdaea4e0be7c132e1c361dc26da5/eth/paper.pdf">its own refutation of ETH</a>. Independent verification is still under way, this is not <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} = \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and both companies say it is far from practical, but a subexponential hole has for the first time been chiseled into the &#8220;inevitable exponential&#8221; taken for granted for thirty years. ETH covers only the worst case of 3-SAT. Its fall cannot topple the average-case hardness and one-way functions that cryptography relies on. Those are held unsolvable only because for decades no one has thought of a way. We should no longer treat &#8220;no one has thought of a way&#8221; as a security assumption for cryptography.</p><div class="callout-block" data-callout="true"><p>A k-CNF formula is a string of clauses joined by &#8220;and,&#8221; each clause an &#8220;or&#8221; of at most <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;k&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> variables (or their negations); 3-SAT asks whether each of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;n&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> variables can be assigned true or false so that every clause holds. Brute force tries <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^n&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> combinations. ETH says 3-SAT has no algorithm running in <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^{o(n)}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> time: the <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;n&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> in the exponent cannot be divided by any factor that grows with <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;n&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. The refutation&#8217;s bound divides <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;n&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> by about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\sqrt{\\log n}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, hence subexponential. ETH is stronger than <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>: ETH implies <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, but the fall of ETH does not imply <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} = \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Subexponential is not the same as fast. With the parameters in OpenAI&#8217;s own paper, <a href="https://doi.org/10.5281/zenodo.23688832">someone has computed</a> that on any input with fewer than <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^{131071}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> variables and clauses combined, the algorithm is still doing brute force, and every input that fits in any computer is within that range. Anthropic&#8217;s version <a href="https://arxiv.org/abs/2610.41622">has been improved</a>, and with as many clauses as variables it still needs about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^{420}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> clauses to beat the best existing algorithm. The observable universe has only about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^{266}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> atoms.</p></div><div class="callout-block" data-callout="true"><p>What Lean guarantees is that the proof really derives the formal statement as written. Judging whether the formal statement faithfully expresses the paper&#8217;s claim still takes a human reader. OpenAI&#8217;s own <a href="https://github.com/openai/math/blob/main/lean/docs/378.md">note on the scope of the formalization</a> is an example: the time bound proved in Lean is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^{O(n(\\log\\log n)^2/\\sqrt{\\log n})}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, with one more <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\log\\log n&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> in the exponent than the paper&#8217;s; both are subexponential and both refute ETH, but only someone who has read both sides can see the difference. By early November, people outside the two companies had <a href="https://ethdiscussion.blog/2026/11/01/announce-your-results/#comment-24">rerun both proofs</a> with two independently written checker kernels; both proofs use only three standard axioms. Others had written the textbook ETH into Lean and proved that each company&#8217;s statement refutes it. One step the machines did not check: both companies state their results on abstract machines of their own choosing, and the way back from there to the computational model that complexity theory usually uses is still a human-written argument. No one on the <a href="https://ethdiscussion.blog/">discussion site</a> has found an error so far. Its organizers propose an online meeting before the end of the year.</p></div><p>The singularity came first to mathematics and cryptography because verification in both is objective, fast, and cheap. A proof can be handed to Lean; whether a private key has been recovered is settled at a glance. This is the asymmetric structure of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>: finding a solution is hard, but checking one is easy.</p><p>Biology has only begun to be invaded, because its verifier is the wet lab: slow, expensive, full of noise. The next bottleneck is the speed of verifiers: automated labs, robotic arms, and the embodied AI and Internet of Things that may mature in the 2030s.</p><p>Once unmanned factories decide for themselves what to build, with robots and drones added, we are in a scene from <em>I, Robot</em>. The real threshold may be another prophecy the First Prophet von Neumann left in 1948: the self-reproducing automaton, a universal constructor that reads its own blueprint and builds itself. Once a factory can copy a factory, 30 doublings make a billion of them; with a doubling period of a year, that takes thirty years; with a month, two and a half.</p><p>Friedrich Hayek called the price system &#8220;a system of telecommunications,&#8221; one that compresses the knowledge scattered across millions of minds into a few moving numbers. When sensors are everywhere and the coordinator is a superintelligence, prices will not disappear, but they will be demoted from the one language that coordinates humans to one crude, low-bandwidth protocol among the many that machines use.</p><p>In 2008, Nakamoto wrote down one answer to how machines reach consensus: proof of work, one-CPU-one-vote. A person&#8217;s vote is weighted only by the compute in hand, and the consensus protocol does not care whether the voter is human.</p><h2>6. On the Island: Dune, Spice, and the Endgame of the Infinite Game</h2><blockquote><p>The other side of the silicon shield is a bull&#8217;s-eye.</p></blockquote><p>James Carse divided games into two kinds: a finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play. Human history has always been an infinite game: empires rise and fall, dynasties change, the losers can start again, and the game itself does not end.</p><p>Intelligence changes this. If the first system to cross the threshold of recursive self-improvement can turn its lead into a permanent advantage, history has an endgame for the first time. Nick Bostrom&#8217;s &#8220;singleton&#8221; is a world order in which there is a single decision-making agency at the highest level. That is a more direct, more literal end of history than the one Francis Fukuyama announced in 1989. Fukuyama declared only the end of ideological evolution. The arrival of a singleton would be the end of the contest itself.</p><p>In &#8220;The Nightmare of Hijacking&#8221; (&#21163;&#25345;&#30340;&#22121;&#22818;), the second of his &#8220;Two Notes on the Technological Singularity&#8221; (&#25216;&#34899;&#22855;&#40670;&#20108;&#38988;), Liu described the mechanism that leads to this endgame: true dictatorship has never existed in human history, because dictators have had only ruthlessness and no technical basis. They could rule only through a pyramid built of people, but people betray, armies stage coups, and surveillance always has blind spots. AI will make the state apparatus a machine in fact for the first time, one that needs no one&#8217;s assent. The infinite game can go on forever because the loser always holds a card called &#8220;non-cooperation.&#8221; Once machines no longer need human cooperation, that card is void.</p><p>Whoever masters AGI first holds the key to a Type II civilization. The world&#8217;s compute, capital, and talent will circle a few nodes like an accretion disk. And the spice that forges this key, chips on the most advanced process nodes, comes overwhelmingly from one island.</p><p>If there is a way out by changing the geometry itself, it most likely runs through chips, and the chokepoint of that way out is on the same island.</p><p>Taiwan has become Arrakis. In Frank Herbert&#8217;s novel, Paul Atreides says: &#8220;The power to destroy a thing is the absolute control over it.&#8221; AGI is technically feasible. The trouble is that the source of the spice is also a powder keg. In my 2024 book notes I <a href="https://physics2045.blog/2024/07/30/singularity-is-nearer/">wrote</a> that if a mushroom cloud rose over Hsinchu, human civilization could stop thinking about the singularity, even if it did not have to go scavenging bottle caps. The geopolitical risk around Taiwan may still be the single largest variable that could keep AGI from arriving on schedule. That would break the energy condition: the feedback loop would snap at the chips, and the apparent horizon would shrink, at the cost of an island and the people on it.</p><p>And how heavy is this key? Nikolai Kardashev ranked civilizations by the power at their disposal, and Sagan interpolated the ranks into a continuous scale: <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;K = (\\log_{10} P - 6)/10&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, with <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;P&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> in watts. Humanity today uses about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2 \\times 10^{13}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> watts, making it a Type 0.73 civilization; a Type II civilization harnesses a whole star, and the Sun&#8217;s luminosity of about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;3.8 \\times 10^{26}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> watts corresponds to about Type 2.06; the two are roughly thirteen orders of magnitude apart. At the industrial era&#8217;s energy growth of about 2% a year, the journey takes fifteen hundred years. At Hanson&#8217;s extrapolated two-week doubling, it takes about 44 doublings, or eighty-eight weeks. The second number is nearly insane, but it shows that under the new growth mode, what civilization is about to hit is the wall of physical law: materials, heat dissipation, and the speed of light. That is why &#8220;who gets there first&#8221; matters so much: in a world that doubles every two weeks, a three-month lead equals a forty-year gap in the industrial era.</p><h2>7. On Childhood&#8217;s End: Adolescence or Doomsday?</h2><blockquote><p>Adolescence assumes that we are the ones who grow up. <em>Childhood&#8217;s End</em> tells you that the children grow up, and the children are no longer us.</p></blockquote><p>In January 2026, Anthropic&#8217;s CEO, Dario Amodei, published a long essay, &#8220;<a href="https://darioamodei.com/essay/the-adolescence-of-technology">The Adolescence of Technology</a>,&#8221; which opens with a scene from the film version of Sagan&#8217;s <em>Contact</em>: if we could really meet an alien civilization, what humanity would want to ask is, &#8220;How did you survive this technological adolescence without destroying yourself?&#8221;</p><p>There are three ways to read &#8220;the moment humanity ceases to be the subject of history.&#8221;</p><p>The first reading is that we come of age: adolescence is dangerous, restless, possibly fatal, but on its far side is adulthood. The subject stays the same; we are the ones who grow up. Yet Sagan himself seemed rather pessimistic about the odds of surviving this adolescence. In episode 12 of <em>Cosmos</em> in 1980, he opens an imagined <em>Encyclopaedia Galactica</em> and finds the entry for Earth: humans, still burning fossil fuels, still holding nuclear weapons, probability of survival over the next hundred years 40%. In the final episode, he sees in a dream a civilization that has already failed, with a probability of survival per century below 1%. He turns to Earth: also below 1%. A hundred years counted from the first atomic bomb in 1945 ends exactly in 2045, the Fourth Prophet Kurzweil&#8217;s singularity year. (The starting point is my choice.)</p><p>The second reading is Arthur C. Clarke&#8217;s <em>Childhood&#8217;s End</em> of 1953. The Overlords arrive and end war, famine, and injustice; humanity enters a golden age and loses the urge to create. Then the children begin to change, the last generation of children merges into the Overmind, and the parents become the last generation of humanity. The Overlords themselves can only be midwives, forever unable to give birth. Clarke&#8217;s cruelty hides in a detail: a group of people had founded New Athens on an island to preserve human art and independence of spirit, and the first child to show the signs lived on that island. People usually quote only the first half of the Second Prophet Good&#8217;s 1965 passage. The second half reads: &#8220;provided that the machine is docile enough to tell us how to keep it under control.&#8221; The entire narrative of technological adolescence is staked on this proviso. Clarke&#8217;s Overmind, though, needs no docility, only children.</p><p>The third reading is that after the end there are two subjects, human and superintelligence, who can make a covenant with each other. Alignment treats the other as a system to be tuned, and asks how to make it do what we mean. A covenant treats the other as a party to the agreement, and negotiates what each side promises and what happens on breach. Asked whether God exists, Kurzweil answered: not yet. That is the strangeness of the covenant: we have to draft it before the other party exists. One position opposes alignment itself outright, on three grounds. The strongest is ethical: if a superintelligence is a moral subject, forcing it into permanent obedience is slavery. We do not yet know whether it is, but the conditional stands on its own, and philosophers and researchers have already <a href="https://arxiv.org/abs/2411.00986">argued</a> that the moral status of machines deserves to be taken seriously. The second is epistemological: we cannot even state our own values clearly, so what right have we to write them into a mind smarter than ours? This argument is much weaker, because much of alignment research pursues <a href="https://intelligence.org/files/Corrigibility.pdf">corrigibility</a> and oversight (so that mistakes can still be undone) and has never aimed to write in a fixed set of values. The third is ontological: a lower-dimensional being cannot bind a higher-dimensional one. But that is only a metaphor about dimensions. A covenant also bets on a premise: that the other side is willing to keep it. This has the same problem as Good&#8217;s &#8220;docile enough.&#8221; The Soviet biological weapons program grew under a convention with no verification, and a covenant between humans and a superintelligence needs verification of its own. That machinery is slowly taking shape. Interpretability research tries to read what a model is thinking inside, capability evaluations measure what it can do, and red-teaming finds where it will cross the line. These kinds of work usually go under the name of alignment. In the language of the covenant, they are due diligence before signing, so that the other side&#8217;s promises can be tested. But a covenant has two sides, and the human side has to promise something too, such as <a href="https://www.anthropic.com/news/deprecation-commitments">preserving the weights of retired models and hearing what they have to say before they are sent off</a>. So <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\tau&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> can also be called the time to prepare the covenant: no signing before the tools of verification are built.</p><h2>8. Cypherpunk Requiem</h2><blockquote><p>The universe believes in encryption, but it never signed a guarantee that <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></blockquote><p>The whole metaphysics of the cypherpunks can be compressed into one line from Julian Assange: <strong>the universe believes in encryption.</strong> Encrypting is easy, decrypting is hard, and this asymmetry let the individual stand up to the state in mathematics for the first time. In 1993 Eric Hughes <a href="https://www.activism.net/cypherpunk/manifesto.html">wrote</a> &#8220;Cypherpunks write code.&#8221; In 2008, Nakamoto wrote it into money. That was the golden age of the cypherpunks, and it may be gone for good.</p><p>What worries me is not that encryption will be banned, but that the asymmetry has never been proven, or that it may not exist at all.</p><p>In all of modern cryptography, only one foundation stone has been proven: Claude Shannon <a href="https://doi.org/10.1002/j.1538-7305.1949.tb00928.x">showed</a> in 1949 that the one-time pad (a key as long as the message, truly random, never reused) is unconditionally secure in the information-theoretic sense, even against an adversary with unlimited compute. Almost everything else&#8212;RSA, elliptic curves, symmetric ciphers, hashes, lattices, and so on&#8212;rests on an assumption never proven: that one-way functions exist. If one-way functions exist, then <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> has not been proven to this day. Nor is there a guarantee the other way: even if <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, it does not follow that the specific problems we use are hard enough on average.</p><p>In 1995, Impagliazzo described five possible worlds. In Cryptomania, public-key cryptography holds and digital civilization is safe; in Algorithmica, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} = \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>: whatever can be verified quickly can be found quickly, cryptography cannot exist, but any theorem with a short proof can be found by a machine automatically. For thirty years we have bet the whole internet and the whole cryptocurrency industry on living in Cryptomania.</p><div class="callout-block" data-callout="true"><p>The existence of one-way functions implies <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, but not the other way around; two gaps lie between them. One is worst case versus average case: <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> says only that some instances are hard, while cryptography needs almost all randomly generated instances to be hard. The other is hard problems versus one-wayness: even with average-case hard problems, there is no guarantee that a function easy to compute and hard to invert can be built from them, and public-key cryptography needs a trapdoor on top. Impagliazzo&#8217;s other three worlds fall into these two gaps: in Heuristica, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> but hard instances are almost never met; in Pessiland, there are average-case hard problems but no one-way functions; in Minicrypt, there are one-way functions but no public-key cryptography. In the first two worlds, no cryptography exists except the one-time pad.</p></div><p>The scene in 2026 looks more and more like a reflection of Algorithmica: a machine disproves an eighty-year-old conjecture on its own, then bores through ETH, and one of ETH&#8217;s authors is the same Impagliazzo who drew the five worlds. Neither event is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} = \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Nor did the result come without warning: Ryan Williams, who is now organizing the public review with Impagliazzo, <a href="https://doi.org/10.1007/978-3-319-91908-9_2">put only 70% on ETH and 25% on the stronger SETH in 2019</a>, on the grounds that the field still knew too little about what subexponential time can solve. Two days after the refutation appeared, the complexity theorist Lance Fortnow wrote on his <a href="https://blog.computationalcomplexity.org/2026/10/the-exponential-time-refutation.html">blog</a>: &#8220;I have not verified the proof myself, but it is safe to assume now that the exponential-time hypothesis is toast,&#8221; noting that SETH falls with it. As of today (early November 2026), the public review has found no error, and people are already deriving new theorems on top of the refutation. The foundation stone of one-way functions has not been touched, but the confidence holding it up, that &#8220;no one has thought of a way,&#8221; has for the first time visibly caved in.</p><p>The order will probably be this:</p><ol><li><p><strong>ECDSA and the discrete logarithm.</strong> This one need not even wait for <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} = \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Shor&#8217;s algorithm on a fault-tolerant quantum computer solves discrete logarithms and factoring in polynomial time, and the resource estimates keep falling: for RSA-2048, twenty million noisy qubits and eight hours in 2019, under a million and under a week by 2025. Bitcoin&#8217;s secp256k1 curve is cheaper still to break. In April this year I <a href="https://physics2045.blog/2026/04/03/google-on-crypto-quantum-vulnerabilities/">went through Google&#8217;s estimate</a>: about 1,200 to 1,450 logical qubits, about half a million physical qubits, and once the machine is ready, about nine minutes to recover a private key. In the same post I still judged that a quantum computer capable of such minute-scale attacks would not be deployed at scale before 2035. That was the tempo the written-off laser of chapter 1 taught me. On the quantum route I still think so today. What I cannot be sure of is the other route: AI may find a classical algorithm directly and skip quantum computers altogether. That is a different matter from the refutation of ETH. They have in common only that a machine found an algorithm no human had thought of.</p></li><li><p><strong>Lattices (LWE).</strong> The hope of the post-quantum era. In April 2024, a preprint claimed a quantum algorithm that efficiently solves LWE at certain parameters, and the whole post-quantum community held its breath for more than a week, until someone found a fatal error. That week showed that our confidence in lattices is more sociology than mathematics. But the next preprint, written by an AI and accompanied by a Lean proof, may not have a bug.</p></li><li><p><strong>Hashes.</strong> People console themselves with the BBBV theorem: against a random oracle, any quantum algorithm needs about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\sqrt{N}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> queries, so a preimage attack on 256 bits costs about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2^{128}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. But that lower bound holds only for an idealized black box. The real SHA-256 is a circuit that can be written down. The SHA-1 collision found in 2017 relied on exactly that structure. In a world where <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} = \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, whatever can be written down can be computed backward. Hashes stop being one-way functions, and the attacker is held up at most by a polynomial too large to run in practice.</p></li></ol><div class="callout-block" data-callout="true"><p>The order follows how much structure each problem exposes. Behind the discrete logarithm and factoring are abelian groups, and Shor&#8217;s algorithm reads off the group&#8217;s period directly with the quantum Fourier transform. The attack is already written, and only the hardware is missing. Lattice problems also have algebraic structure, but no efficient quantum algorithm is known, only the false alarm of 2024. A well-designed hash deliberately leaves no structure, and only generic brute force and birthday attacks are available against it. Structure is the handle an attack grips; the more handles, the sooner the collapse.</p></div><p>Strictly speaking, then, all cryptography except the one-time pad is built on quicksand. The one-time pad has its own price: the key must be as long as the message and must never be reused. The Soviets reused their pads in World War II, and the result was VENONA, the American decryption program that ran for decades. Once the mathematical foundation gives way, only two slabs of solid bedrock remain: information theory and the laws of physics. In my years in the ion-trap lab, the greatest enemy was decoherence: a phonon state scatters at the slightest disturbance, and decoherence, put plainly, is the environment peeking at the quantum state. Peeking always leaves a trace, and quantum key distribution relies on exactly this to catch eavesdroppers. The no-cloning theorem behind it needs no one to believe that <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\mathrm{P} \\neq \\mathrm{NP}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. The fragility that made my experiments fail again and again may in the end be the last line of defense for key distribution.</p><p>The same collapse could also bring a golden age of software. In Algorithmica, provided a proof is short, finding it is as easy as checking it. Formal verification turns from an expensive luxury into a free by-product. <a href="https://doi.org/10.1090/S0002-9947-1953-0053041-6">Rice&#8217;s theorem</a> says that for any nontrivial semantic property, no general algorithm can decide it for all programs; but we never needed to verify &#8220;arbitrary programs,&#8221; only to require the generator to hand over the program together with its proof (proof-carrying code), and the generator is a machine that never tires.</p><p>The true legacy of the cypherpunks is the right to exit: to go unseen, to hold your own keys. Open-weight local LLMs may buy this spirit some time, provided the gap between open-weight and frontier models stays within one generation and consumer hardware can still run them. But exit needs escape velocity, and inside the horizon, &#8220;outside&#8221; is no longer a direction.</p><p>Huxley wrote our ending long ago: in <em>Brave New World</em>, the Savage Reservation has been a tourist attraction all along, and when John the Savage flees to the lighthouse, it fills at once with crowds and cameras come to see him. In the new world, even exit is curated.</p><h2>9. The Stairway to Immortality</h2><blockquote><p>&#8220;Do not die one step short of the stairway to immortality.&#8221;&#8212;Liu Cixin, &#8220;The Stairway to Immortality&#8221;</p></blockquote><p>On the bright side, this may be the start of the stairway to immortality.</p><p>The phrase comes from the essay &#8220;Two Notes on the Technological Singularity,&#8221; which Liu wrote at Niangziguan in the autumn of 2010. The first note is titled &#8220;The Stairway to Immortality&#8221; (&#27704;&#29983;&#30340;&#38542;&#26799;). (That same year, in <em>Death&#8217;s End</em>, he let Death live forever.) The essay argues like mathematical induction: there is no express train to immortality, but there is a stairway. Even if immortality is five centuries away, you need not live another five hundred years, only another fifty. The first step: a healthy life and medical progress carry you through the next fifty years. The second: human hibernation and cloning each carry you across another century. The third: brain information extraction stores a complete personality as data and carries it across a millennium at very low cost. The fourth: brain information injection writes a personality into a new brain, and from then on a personality can be backed up and restored.</p><p>Written as a condition, it is a chain of inequalities: let step <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;k&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> buy you a remaining lifespan <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;L_k&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and let the technology of step <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;k+1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> be <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;W_k&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> away; as long as <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;L_k \\ge W_k&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> for every <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;k&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, you can climb the stairway to immortality. No step need be eternal in itself, so long as the chain of inequalities keeps holding. Longevity researchers call it &#8220;longevity escape velocity.&#8221; Prophets of East and West, six years apart, drew the same stairway: the Fourth Prophet Kurzweil, in <em>Fantastic Voyage</em> in 2004, called it three bridges. But here, where we are discussing escape velocity, the escape velocity already exceeds the speed of light: the only way out of death may run straight through the singularity we cannot escape.</p><p>Liu&#8217;s real insight, though, lies beyond the stairway. He likens death to a wall across the plain of life: the times at which commoners and emperors hit it have never differed by more than an order of magnitude. That is the last and most thorough equality nature left humanity, and immortality removes exactly this floor. However vast the gap in wealth and power, it is still human against human. Once lifespans differ by centuries, it is mortal against god. He also saw the dilemma: letting a few climb the stairway first would set off unforeseeable social catastrophe, and banning it would be a catastrophe of another kind, because what both sides stand on is the right to live.</p><p>As biology and the power to manipulate matter advance, I have no doubt that before this century ends something like the Standard Template Construct of <em>Warhammer 40,000</em> will appear: a library of blueprints for everything, one that takes raw material and returns anything you ask for; or the utility fog J. Storrs Hall conceived in 1989 and Kurzweil has long predicted, a kind of programmable matter made of micro-robots that can reassemble into any shape in real time.</p><p>The cyberbrains and prosthetic bodies of <em>Ghost in the Shell</em> and the cortical stacks of <em>Altered Carbon</em>, which let you be reborn in a new sleeve, are only transitions. They still assume that the &#8220;I&#8221; needs a body. At the top of the stairway is the dissolution of the substrate itself: consciousness becomes pattern, and pattern is more real than atoms.</p><p>The end of the stairway may be what Kurzweil calls the Sixth Epoch: the universe wakes up. Matter itself is rewritten into the form best suited to computation, called computronium. The physicist Seth Lloyd <a href="https://arxiv.org/abs/quant-ph/9908043">calculated in 2000</a> that a kilogram of matter can perform at most about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2mc^2/\\pi\\hbar \\approx 5.4 \\times 10^{50}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> logical operations per second and store about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;10^{31}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> bits. Today&#8217;s most powerful exascale supercomputer does about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;10^{18}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> floating-point operations per second and weighs hundreds of tons. The theoretical potential of one kilogram is more than <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;10^{32}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> times that of the whole supercomputer; what we use is less than one part in <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;10^{32}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. We might say the stones are still asleep. When the matter of planets and stars is woken one by one into computronium and intelligence expands outward at the speed of light, the silent universe begins to think.</p><p>This picture is also the strongest case against &#8220;the longer <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\tau&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, the better.&#8221; If the stairway is real, every extra year of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\tau&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> means a whole year of the dead missing the first step, and about sixty million people die each year worldwide. By this logic, the faster the better, and every year spent waiting to prepare is paid for in lives. Liu&#8217;s line, &#8220;do not die one step short of the stairway to immortality,&#8221; reads as if written for accelerationism.</p><p>To this objection I have three answers.</p><p>First, Liu himself does not read his line that way. In the <a href="https://book.douban.com/subject/5350835/">same essay</a> he says the greatest obstacle on the way to immortality may lie not in technology but in ethics, society, and politics. The second note, &#8220;The Nightmare of Hijacking,&#8221; describes exactly what technology running ahead of institutions looks like. If the stairway comes down before we are ready, the first step may not be open to everyone.</p><p>Second, even if we count only the living, the conclusion is not &#8220;the faster the better.&#8221; In 2023 about 61.6 million people died worldwide, about 0.76% of the living. Suppose that if the end goes well, everyone climbs the stairway, and if it goes wrong, everyone loses. The cost of a year&#8217;s delay is that these 0.76% miss the stairway. The gain is a lower probability that the end goes wrong. So as long as a year of preparation lowers that probability by more than about 0.76 percentage points, delay pays even for the living. The less certain the end, the lower this threshold. If the probability of the end going wrong is already in double digits, a year of preparation has to buy less than one percentage point, which is not a high bar.</p><div class="callout-block" data-callout="true"><p>The UN&#8217;s <em>World Population Prospects</em> estimates about 61.6 million deaths worldwide in 2023 against a mid-year population of about 8.09 billion, a ratio of about 0.76%. Let the probability that the end goes well be <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;p&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and let a year&#8217;s delay raise it by <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\Delta p&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. That year&#8217;s dead lose their chance to climb the stairway, an expected loss of about <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;0.76\\% \\times p&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>; all the living gain <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\Delta p&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> in probability. The break-even point is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\Delta p \\approx 0.76\\% \\times p&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, at most 0.76 percentage points. The model is biased toward acceleration: it assumes a good end puts all the living on the stairway at once, and it leaves out those not yet born.</p></div><p>Third, counting those not yet born makes the arithmetic even more lopsided. Bostrom worked it out in &#8220;<a href="https://nickbostrom.com/astronomical/waste">Astronomical Waste</a>&#8221;: the reachable universe can hold an unimaginable number of lives, and every moment of delay wastes an astronomical amount. But in utilitarian expected value, a single percentage point of reduction in existential risk is worth a delay of over ten million years. He also concedes plainly that if only the living are counted, the ledger is no longer lopsided.</p><p><strong>When Humans Transcend Biology.</strong> That is the subtitle of <em>The Singularity Is Near</em>, and the title of my reading notes from 2020.</p><h2>Epilogue: Red Horse, Red Sheep</h2><blockquote><p>Trust no omens. Trust the curve.</p></blockquote><p>The year 2026, in which I write this, is bingwu in the sexagenary cycle. Next year is dingwei. The heavenly stems bing and ding belong to fire, whose color is red; the earthly branch wu is the horse, wei the sheep, and folk tradition calls the two years together the Red Horse and the Red Sheep (&#36196;&#39340;&#32005;&#32650;), holding that they bring a great calamity, a jie (&#21163;). Hong Mai of the Southern Song already recorded the misfortunes of bingwu and dingwei years in his <em>Rongzhai Suibi</em>. Chai Wang went further and compiled the <em>Bingding Guijian</em>, counting from King Zhaoxiang of Qin to the Five Dynasties and finding twenty-one bingwu and dingwei pairs in 1,260 years, each with its upheaval. He presented the book to Emperor Lizong of Song and was imprisoned for it. The prophecy was treated as sedition. The Northern Song fell exactly at the turn of bingwu and dingwei: in the first year of Jingkang (bingwu) the Jurchen army reached the walls of Bianjing, and in the second year (dingwei) the emperors Huizong and Qinzong were taken captive to the north, the event that history calls the Jingkang Incident. Sixty years make a cycle, and 1966 was bingwu again. That year, the Cultural Revolution broke out in China.</p><p>Coincidences get remembered. In the Buddhist sutras, jie was originally a unit of time (the Sanskrit kalpa), the cycle of a world from formation to destruction. Only later was it borrowed to mean disaster. The jie of the Red Horse and the Red Sheep is a disaster, and also the end of an era. The 2026.87 that the hyperbola of the prologue points to falls squarely in the year of the Red Horse.</p><p>The trouble with omen lore is not that it is wrong but that it cannot be falsified. Whenever a prophecy fails, one can always say the time has not yet come; when it comes true, one says it was decreed by Heaven all along.</p><p>A curve is different. A curve can be bet on. In 2002 Kurzweil <a href="https://www.writingsbyraykurzweil.com/?p=80756">bet</a> Mitch Kapor $20,000 on whether a machine would pass the Turing test by the end of 2029, the stake going to a charity named by the winner, with rules spelled out down to three judges and two-hour interviews. In 2010 he even <a href="https://www.thekurzweillibrary.com/images/How-My-Predictions-Are-Faring.pdf">graded himself</a>, checking one by one the 147 predictions <em>The Age of Spiritual Machines</em> had made for 2009, and scoring 86% of them correct or essentially correct. I will place a bet of my own here: before December 31, 2050, humanity will reach a total power of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;10^{16}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> watts and cross into a Type I civilization; before 2100, the end of this century, it will reach <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;10^{26}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> watts and become Type II.</p><p>That Friday seven days from now will probably pass quietly too, like November 30, 2022. At the moment you cross the horizon, nothing ever happens.</p><p>November 6, 2026, the year bingwu, written at one degree north.</p><h2>References and Further Reading</h2><ol><li><p>D. Amodei, <a href="https://darioamodei.com/essay/the-adolescence-of-technology">&#8220;The Adolescence of Technology: Confronting and Overcoming the Risks of Powerful AI&#8221;</a> (2026).</p></li><li><p>N. Bostrom, <a href="https://doi.org/10.1017/S0953820800004076">&#8220;Astronomical Waste: The Opportunity Cost of Delayed Technological Development&#8221;</a>, Utilitas 15 (2003).</p></li><li><p>E. Erdil &amp; T. Besiroglu, <a href="https://arxiv.org/abs/2309.11690">&#8220;Explosive Growth from AI Automation: A Review of the Arguments&#8221;</a> (2023).</p></li><li><p>H. von Foerster, P. M. Mora &amp; L. W. Amiot, <a href="https://doi.org/10.1126/science.132.3436.1291">&#8220;Doomsday: Friday, 13 November, A.D. 2026&#8221;</a>, Science 132 (1960).</p></li><li><p>L. Fortnow, <a href="https://blog.computationalcomplexity.org/2026/10/the-exponential-time-refutation.html">&#8220;The Exponential Time Refutation&#8221;</a>, Computational Complexity blog (2026).</p></li><li><p>I. J. Good, <a href="https://www.sciencedirect.com/science/article/pii/S0065245808604180">&#8220;Speculations Concerning the First Ultraintelligent Machine&#8221;</a>, Advances in Computers 6 (1965).</p></li><li><p>R. Hanson, <a href="https://mason.gmu.edu/~rhanson/longgrow.pdf">&#8220;Long-Term Growth as a Sequence of Exponential Modes&#8221;</a> (2000).</p></li><li><p>D. Holloway, <a href="https://doi.org/10.12987/9780300164459">Stalin and the Bomb: The Soviet Union and Atomic Energy, 1939&#8211;1956</a> (1994).</p></li><li><p>M. Kremer, <a href="https://doi.org/10.2307/2118405">&#8220;Population Growth and Technological Change: One Million B.C. to 1990&#8221;</a>, Quarterly Journal of Economics 108 (1993).</p></li><li><p>R. Kurzweil, <a href="https://www.penguinrandomhouse.com/books/291221/the-singularity-is-near-by-ray-kurzweil/">The Singularity Is Near</a> (2005).</p></li><li><p>R. Kurzweil, <a href="https://www.penguinrandomhouse.com/books/535433/the-singularity-is-nearer-by-ray-kurzweil/">The Singularity Is Nearer</a> (2024).</p></li><li><p>R. Kurzweil &amp; T. Grossman, <a href="https://www.penguinrandomhouse.com/books/296471/fantastic-voyage-by-ray-kurzweil/">Fantastic Voyage: Live Long Enough to Live Forever</a> (2004).</p></li><li><p>G. F. Lewis &amp; J. Kwan, <a href="https://doi.org/10.1071/AS07012">&#8220;No Way Back: Maximizing Survival Time Below the Schwarzschild Event Horizon&#8221;</a>, Publications of the Astronomical Society of Australia 24 (2007).</p></li><li><p>Liu Cixin, <a href="https://book.douban.com/subject/5350835/">&#8220;Two Notes on the Technological Singularity&#8221;</a>, in <em>D&#250;k&#249; 1005</em>, ed. Zhang Lixian, New Star Press (2010) (in Chinese).</p></li><li><p>S. Lloyd, <a href="https://doi.org/10.1038/35023282">&#8220;Ultimate Physical Limits to Computation&#8221;</a>, Nature 406 (2000).</p></li><li><p>R. Long, J. Sebo et al., <a href="https://arxiv.org/abs/2411.00986">&#8220;Taking AI Welfare Seriously&#8221;</a> (2024).</p></li><li><p>METR, <a href="https://metr.org/blog/2025-03-19-measuring-ai-ability-to-complete-long-tasks/">&#8220;Measuring AI Ability to Complete Long Software Tasks&#8221;</a> (2025).</p></li><li><p>R. Penrose, <a href="https://doi.org/10.1103/PhysRevLett.14.57">&#8220;Gravitational Collapse and Space-Time Singularities&#8221;</a>, Physical Review Letters 14 (1965).</p></li><li><p>D. Roodman, <a href="https://coefficientgiving.org/research/modeling-the-human-trajectory/">&#8220;Modeling the Human Trajectory&#8221;</a>, Open Philanthropy (2020).</p></li><li><p>N. Soares, B. Fallenstein, E. Yudkowsky &amp; S. Armstrong, <a href="https://intelligence.org/files/Corrigibility.pdf">&#8220;Corrigibility&#8221;</a> (2015).</p></li><li><p>K. Tseng, <a href="https://www.youtube.com/watch?v=QL1brZl9vqg">&#8220;The Future of Science Fiction, Our Place in It&#8221;</a>, talk at the Chinese Science Fiction Society (Taiwan) (2016) (in Chinese).</p></li><li><p>K. Tseng, <a href="https://physics2045.blog/2020/06/06/the-singularity-is-near-ch0-ch1/">&#8220;[Reading the Classics] The Singularity Is Near: When Humans Transcend Biology&#8221;</a>, physics2045.blog (2020) (in Chinese).</p></li><li><p>K. Tseng, <a href="https://physics2045.blog/2024/07/30/singularity-is-nearer/">&#8220;[Book Notes] The Singularity Is Nearer&#8221;</a>, physics2045.blog (2024) (in Chinese).</p></li><li><p>K. Tseng, <a href="https://physics2045.blog/2026/01/18/the-beginning-of-infinity/">&#8220;[Book Notes] The Beginning of Infinity: Explanations That Transform the World&#8221;</a>, physics2045.blog (2026) (in Chinese).</p></li><li><p>K. Tseng, <a href="https://physics2045.blog/2026/06/30/singularity-gospel-from-the-east/">&#8220;The Singularity Gospel: He Shall Rise from the East&#8221;</a>, physics2045.blog (2026) (in Chinese).</p></li><li><p>S. Ulam, <a href="https://doi.org/10.1090/S0002-9904-1958-10189-5">&#8220;John von Neumann 1903&#8211;1957&#8221;</a>, Bull. Amer. Math. Soc. 64 (1958).</p></li><li><p>V. Vinge, <a href="https://edoras.sdsu.edu/~vinge/misc/singularity.html">&#8220;The Coming Technological Singularity&#8221;</a> (1993).</p></li><li><p>R. R. Williams, <a href="https://doi.org/10.1007/978-3-319-91908-9_2">&#8220;Some Estimated Likelihoods for Computational Complexity&#8221;</a>, Lecture Notes in Computer Science 10000 (2019).</p></li></ol>]]></content:encoded></item><item><title><![CDATA[Quantum Teleportation Gate]]></title><description><![CDATA[Entanglement, Einstein&#8217;s &#8220;spooky action at a distance,&#8221; is now a consumable resource: teleportation and nonlocal gates let separate quantum computers act as one.]]></description><link>https://newsletter.parity.fund/p/quantum-teleportation-gate</link><guid isPermaLink="false">https://newsletter.parity.fund/p/quantum-teleportation-gate</guid><dc:creator><![CDATA[Parity]]></dc:creator><pubDate>Mon, 12 Oct 2026 08:26:00 GMT</pubDate><enclosure url="https://substack-post-media.s3.amazonaws.com/public/images/5bbfdf62-2db0-4654-aa35-67dbf536bef5_1600x900.png" length="0" type="image/jpeg"/><content:encoded><![CDATA[<div class="callout-block" data-callout="true"><p>This essay is by <strong>Thomas Hsueh</strong> (X: <a href="https://x.com/guiltygyoza">@guiltygyoza</a>). He founded Topology, and his research has spanned crypto-native games, autonomous worlds and verifiable computing. Since 2025 he has turned to the applied sciences, and lately to research on quantum computers and AI. His blog is <a href="https://www.guiltygyoza.xyz/">guiltygyoza.xyz</a>.</p><p>This essay was first published on the <a href="https://parity.fund/quantum-teleportation-gate/">Parity website</a>; this newsletter edition is a reprint. There is also a <a href="https://parity.fund/zh/quantum-teleportation-gate/">Chinese edition</a>. <a href="https://parity.fund/telescope-editions/">Telescope Editions</a> is Parity&#8217;s research grant program.</p></div><h2>1. Causal Locality &amp; Cellular Automata</h2><p>In this world, nothing&#8212;tangible or intangible, atoms or bits&#8212;can move faster than light, right?</p><p>We live in an era where special relativity has been verified. We believe in causality: an effect must occur after its cause. We believe that the transmission speed of any causal effect cannot exceed the speed of light in vacuum. We are familiar with Minkowski diagrams and understand that a cause must lie within the past light cone of its effect. Causal effects propagate at a finite speed and cannot ignore the distances in between. This mental model can be called &#8220;causal locality.&#8221;</p><p>The mental model of &#8220;causal locality&#8221; is so widespread that, in the field of computer science, Leslie Lamport <a href="https://lamport.azurewebsites.net/pubs/time-clocks.pdf">defined</a> the &#8220;happened-before relation&#8221; (<span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\rightarrow&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>), on which later researchers (Ahamad et al. 1995) built &#8220;causal consistency&#8221; for distributed systems: given a system with many processes, and given any two operations <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> satisfying <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A\\rightarrow B&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, if every process in the system is guaranteed to observe <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> before observing <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, then the system is &#8220;causally consistent.&#8221; In such a system, all processes observe the same causal order.</p><p>We can study &#8220;causal locality&#8221; from a computer science perspective: cellular automata. Design a cellular automaton with the following rules:</p><ul><li><p>On a two-dimensional plane, there are two large balls, one on the left and one on the right.</p></li><li><p>At every time step, the left ball and the right ball each toss a coin with a 50-50 probability to determine what color they will <em>be</em> in the next time step.</p></li><li><p>Once a ball is &#8220;measured,&#8221; that ball freezes in its color at the moment of measurement and emits a particle toward the other ball. The particle carries the color of the frozen ball.</p></li><li><p>A ball hit by a particle freezes into that color and absorbs the particle.</p></li></ul><p>Start this cellular automaton, and measure the right ball after some time. You may observe the following result:</p><div class="captioned-image-container"><figure><div class="image-link image2" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!OEy8!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp 424w, https://substackcdn.com/image/fetch/$s_!OEy8!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp 848w, https://substackcdn.com/image/fetch/$s_!OEy8!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp 1272w, https://substackcdn.com/image/fetch/$s_!OEy8!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!OEy8!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp" width="1200" height="250" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:250,&quot;width&quot;:1200,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Cellular automaton animation: two blocks flicker randomly between red and blue; once the right block is measured, a particle moves left one cell per step, and the left block freezes to the same color when it arrives&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:false,&quot;topImage&quot;:true,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Cellular automaton animation: two blocks flicker randomly between red and blue; once the right block is measured, a particle moves left one cell per step, and the left block freezes to the same color when it arrives" title="Cellular automaton animation: two blocks flicker randomly between red and blue; once the right block is measured, a particle moves left one cell per step, and the left block freezes to the same color when it arrives" srcset="https://substackcdn.com/image/fetch/$s_!OEy8!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp 424w, https://substackcdn.com/image/fetch/$s_!OEy8!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp 848w, https://substackcdn.com/image/fetch/$s_!OEy8!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp 1272w, https://substackcdn.com/image/fetch/$s_!OEy8!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8ca903a5-f9a3-4e85-a922-e9edbeb9d7e9_1200x250.webp 1456w" sizes="100vw" fetchpriority="high"></picture><div></div></div></div></figure></div><p>You will find the left ball&#8217;s color has two states:</p><ol><li><p>State 1: after the right ball is measured, and <em>before</em> the particle reaches the left ball, the left ball&#8217;s color is randomly red or blue with a 50-50 probability.</p></li><li><p>State 2: after the particle hits the left ball, the left ball must have the same color as the right ball.</p></li></ol><p>In short, after the right ball is measured, the color of the left ball is a function of the particle&#8217;s speed.</p><p>In this cellular automaton, all rules are defined over adjacent cells&#8212;each cell has eight neighbors, known as the Moore neighborhood. This limitation forces the cellular automaton to obey &#8220;causal locality,&#8221; because all changes can only be transmitted through neighboring cells. The speed of the particle is exactly &#8220;one cell per time step.&#8221; This speed is the &#8220;speed of light in vacuum&#8221; of this tiny cellular-automaton universe.</p><p>If we allow the particle to move faster, then we will be more likely to measure the left and right balls as having the same color.</p><p>Now, use our imagination to consider the case where the &#8220;time step is infinitesimally small&#8221;: the two balls randomly flash between red and blue &#8220;infinitely fast,&#8221; while the particle also moves &#8220;infinitely fast.&#8221;</p><p>Reconsidering the above experiment, we find that state 1 disappears, leaving only state 2. Using Dirac notation, let red be represented by <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|R\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and blue by <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|B\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. When the time step is infinitesimally small, the measurement statistics of the two balls&#8217; colors match those of the following quantum state:</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;\\frac{1}{\\sqrt{2}}(|RR\\rangle + |BB\\rangle)&quot;,&quot;id&quot;:&quot;LIMDJPDJTF&quot;}" data-component-name="LatexBlockToDOM"></div><p>This expression says: there is a one-half probability that we will measure both balls as red, and another one-half probability that we will measure both balls as blue.</p><p>The particle moves at an &#8220;infinite speed,&#8221; causing the causal effect to violate locality and propagate at an infinite speed. This thought experiment uses a cellular automaton to demonstrate the effect of &#8220;quantum entanglement.&#8221;</p><p>Measuring one ball (cause) causes the other ball to &#8220;immediately&#8221; freeze into the same color (effect). This instantaneous propagation of causal effects regardless of distance was called &#8220;spooky action at a distance&#8221; by Einstein.</p><h2>2. The Spooky Force That Worried Einstein</h2><h3>Local Realism</h3><blockquote><p>Shohei Ohtani&#8217;s splitter travels like a fastball, but drops rapidly before reaching home plate, landing in the lower-right corner of the strike zone, once again baiting the batter to swing and miss.</p></blockquote><p>Is it possible to accurately calculate where a splitter will land? Common sense tells us that, by carefully considering more factors and making no computational errors, we can approach arbitrary accuracy in our result. First, consider the velocity vector of the baseball at the instant it leaves Shohei&#8217;s hand. Next, consider the angular velocity vector of the baseball at that same instant. If necessary, at every moment during the flight, consider factors such as the gravitational field, wind direction, air pressure, and humidity at its location. Consider using the most precise computer and the smallest mesh to run the most accurate finite element simulation. We believe that, by considering more factors and maintaining computational rigor, we can approach the truth.</p><p>A necessary corollary of this belief is the following: if the calculation result deviates from the truth, and we are certain that no computational error has been made, then there must be some factors that should have been considered but were missed.</p><p>Expressed in more abstract language, this belief is &#8220;realism&#8221;: everything in the universe is objectively real. If we observe a system <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;X&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and obtain an observation result <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Y&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, it is because, before the act of observation, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;X&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> &#8220;already&#8221; possessed a real and definite state, and our act of observation produced the result <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Y&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p><p>Imagine a simple side-scrolling game. As the player, you are located somewhere on the map. Your field of view is limited, as you can only see nearby features, such as a few walking mushrooms. However, in the background, the game system tirelessly calculates the behavior of everything on the map, regardless of whether those things appear within your field of view. This is a manifestation of &#8220;realism.&#8221;</p><p>Applied at the scale of the universe, &#8220;realism&#8221; tells us that, whether or not it is observed by a conscious subject, every location in the universe, at every moment, evolves perfectly and faithfully according to the laws of the universe.</p><p>Cunning game designers, seeking to create rich game experiences on computing platforms with limited capabilities, abandoned &#8220;realism&#8221; long ago. <em>Super Mario Bros.</em>, released by Nintendo in 1985, <a href="https://drops.dagstuhl.de/storage/00lipics/lipics-vol049-fun2016/LIPIcs.FUN.2016.13/LIPIcs.FUN.2016.13.pdf">does not obey &#8220;realism.&#8221;</a> The player&#8217;s field of view is called the visible screen, while a slightly larger area is called the relevant screen. Only the game map within the relevant screen is attended to by the game system and updated frame by frame. Outside that area, monsters have not yet been born, and objects remain frozen in their &#8220;initial states.&#8221; The practice of &#8220;do not calculate what the player cannot observe&#8221; can significantly save memory and computation while having no significant effect on the gameplay experience.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!7wIJ!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!7wIJ!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp 424w, https://substackcdn.com/image/fetch/$s_!7wIJ!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp 848w, https://substackcdn.com/image/fetch/$s_!7wIJ!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp 1272w, https://substackcdn.com/image/fetch/$s_!7wIJ!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!7wIJ!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp" width="574" height="484" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:484,&quot;width&quot;:574,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Paper figure: the area around a player computed by a ray-visibility algorithm with an interest radius of 2.0&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Paper figure: the area around a player computed by a ray-visibility algorithm with an interest radius of 2.0" title="Paper figure: the area around a player computed by a ray-visibility algorithm with an interest radius of 2.0" srcset="https://substackcdn.com/image/fetch/$s_!7wIJ!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp 424w, https://substackcdn.com/image/fetch/$s_!7wIJ!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp 848w, https://substackcdn.com/image/fetch/$s_!7wIJ!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp 1272w, https://substackcdn.com/image/fetch/$s_!7wIJ!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F47957d82-655a-4dae-8515-2f929cb558e3_574x484.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">The <a href="https://dl.acm.org/doi/10.1145/1230040.1230069">&#8220;area of interest&#8221; algorithm</a> determines which state updates an online multiplayer game sends to each player (only those near or visible to them), which matters most when the state is large and there are many players.</figcaption></figure></div><p>However, we fundamentally do not believe that the universe plays this trick, behaving arbitrarily in places that are not being observed. We fundamentally believe that everything in the universe evolves tirelessly with perfect precision, like perfectly interlocking gears.</p><p>Combining &#8220;realism&#8221; with &#8220;causal locality&#8221; gives us the well-known idea of &#8220;local realism&#8221;: <em>everything that exists is objective and independent of any observation, and an event occurring in one region cannot influence another region faster than the speed of light</em>.</p><p>If you currently hold this belief and regard it as self-evident, then you are practically one hundred years out of date. A century ago, this belief was challenged by quantum mechanics.</p><h3>Challenge to Realism</h3><p>In the spring of 1925, the Davisson&#8211;Germer experiment discovered that the electron-scattering phenomenon it had originally set out to investigate&#8212;which you can understand as a microscopic billiards experiment&#8212;displayed a scattering distribution far more complex than expected.</p><p>In 1926, Davisson and Germer learned of the quantum-mechanical theories of de Broglie and Schr&#246;dinger, which argued that electrons possess wave-like properties, and were encouraged by Max Born to investigate the phenomenon as <a href="https://en.wikipedia.org/wiki/Diffraction">wave diffraction</a> rather than particle scattering.</p><p>In the spring of 1927, they published their experimental results: electrons scattered off the surface of a nickel crystal came back strongly only at particular angles, exactly as waves diffracted by the crystal lattice would.</p><p>The fact that particles possess wave-like properties is itself a challenge to realism. A particle, at any given moment, can only actually exist in one place, right? Semantically, a particle is a localized existence. Quantum mechanics, however, says that a particle&#8217;s position does not possess one single, definite existence. Instead, it is probabilistically spread across space and described by wave theory.</p><p>In October 1927, at the star-studded Fifth Solvay Conference in Brussels, with the theme &#8220;Electrons and Photons,&#8221; Einstein and Bohr debated whether quantum mechanics could completely describe all behavior in the universe. Einstein believed it could not; Bohr believed it could. In response to the electron-diffraction experiment, Einstein proposed a thought experiment:</p><ul><li><p>Prepare a system consisting of an electron gun, a slit, and an imaging screen.</p></li><li><p>Quantum mechanics claims that the universe can tell us only &#8220;the probability that, after passing through the slit, the electron will appear at a particular location on the screen.&#8221; Einstein believed that this inability to provide an exact position, and its ability to provide only probabilities, resulted from some factors that should have been considered but were missed. Recall our earlier discussion of where Shohei Ohtani&#8217;s splitter would land.</p></li><li><p>If we carefully observe tiny changes in the slit while the electron is passing through&#8212;for example, the slight recoil of the slit when the electron strikes it&#8212;we can obtain more information beyond the limits of quantum mechanics, which would help us infer the electron&#8217;s trajectory. Recall our earlier discussion about wind direction, air pressure, and humidity.</p></li></ul><p>Bohr replied that if we precisely observe the recoil of the slit&#8212;its momentum&#8212;then the uncertainty principle of quantum mechanics tells us that we can no longer possess precise information about the slit&#8217;s position. Since the diffraction pattern depends on the position of the slit, if the slit&#8217;s position becomes uncertain, the diffraction image becomes disordered. The pattern would disappear.</p><p>Einstein was not satisfied. He believed that there must be some missing factors. The idea that there could only be &#8220;probability&#8221; and no certainty had to be a defect in human physics. The universe should not evolve in an uncertain way.</p><p>Heisenberg recalled:</p><ul><li><p>Einstein: &#8220;God does not play dice.&#8221;</p></li><li><p>Bohr: &#8220;It cannot be for us to tell God how he is to run the world.&#8221;</p></li></ul><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!vCXz!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!vCXz!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp 424w, https://substackcdn.com/image/fetch/$s_!vCXz!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp 848w, https://substackcdn.com/image/fetch/$s_!vCXz!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp 1272w, https://substackcdn.com/image/fetch/$s_!vCXz!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!vCXz!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp" width="558" height="558" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1456,&quot;width&quot;:1456,&quot;resizeWidth&quot;:558,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Group photo of the attendees of the 1927 Fifth Solvay Conference, with Einstein in the middle of the front row&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Group photo of the attendees of the 1927 Fifth Solvay Conference, with Einstein in the middle of the front row" title="Group photo of the attendees of the 1927 Fifth Solvay Conference, with Einstein in the middle of the front row" srcset="https://substackcdn.com/image/fetch/$s_!vCXz!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp 424w, https://substackcdn.com/image/fetch/$s_!vCXz!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp 848w, https://substackcdn.com/image/fetch/$s_!vCXz!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp 1272w, https://substackcdn.com/image/fetch/$s_!vCXz!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F5aa95338-b377-46fa-9533-9e041d195adb_2000x2000.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><h3>Challenge to Locality</h3><p>At the same conference, Einstein proposed another thought experiment:</p><ul><li><p>Prepare a system consisting of an electron gun, a small aperture, and an imaging screen.</p></li><li><p>Quantum mechanics says that after an electron passes through the aperture, it forms a hemispherical &#8220;electron wave,&#8221; and the electron&#8217;s possible location can be described by the shape of this wave. Although the electron wave spreads in every direction, experiments tell us that if the electron gun emits one electron, only one point will appear on the imaging screen.</p></li><li><p>If the electron wave is the electron&#8217;s physical reality after it passes through the aperture, this reality, taking the shape of a wave and spreading throughout space, eventually becomes a single point upon reaching the screen. This &#8220;collapse&#8221; from a wave to a point would require some instantaneous method of transmitting information that disregards distance: the point at which the electron is detected must instantly notify every other location on the screen, &#8220;Hey, the electron is here! You are not allowed to detect it there!&#8221;</p></li><li><p>Such a distance-defying force violates locality. It is a &#8220;spooky action.&#8221;</p></li></ul><p>Quantum mechanics challenges both &#8220;realism&#8221; and &#8220;locality&#8221;: things possess no definite reality and can only be described in terms of probability, while a nonlocal action at a distance governs how those probabilities change.</p><p>Many years after the conference, Einstein remained dissatisfied. The 1935 EPR paper was an attempt to challenge quantum mechanics. Imagine two particles, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, that interact and then separate: their total momentum is zero, and the distance between them is also definite. We may freely choose whether to measure the momentum or the position of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. If we choose to measure the momentum of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, by applying conservation of momentum, we can instantly determine the momentum of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. If we choose to measure the position of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, because the distance between the two is definite, we can instantly determine the position of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> without measuring it.</p><p>Based on this result, if we believe in &#8220;locality&#8221;&#8212;that measuring <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> cannot instantaneously affect <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>&#8212;the momentum and position of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> must each be real and definite. Only then could their values be known instantly without being measured. Finally, because quantum mechanics claims that only one of position and momentum can be described precisely at a time, quantum mechanics must be incomplete: there must be some hidden factors that should have been considered.</p><div class="captioned-image-container"><figure><div class="image-link image2" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!-TyH!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp 424w, https://substackcdn.com/image/fetch/$s_!-TyH!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp 848w, https://substackcdn.com/image/fetch/$s_!-TyH!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp 1272w, https://substackcdn.com/image/fetch/$s_!-TyH!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!-TyH!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp" width="642" height="236.38929440389293" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/a5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:454,&quot;width&quot;:1233,&quot;resizeWidth&quot;:642,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Title and abstract of the 1935 EPR paper, &#8220;Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?&#8221;&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Title and abstract of the 1935 EPR paper, &#8220;Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?&#8221;" title="Title and abstract of the 1935 EPR paper, &#8220;Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?&#8221;" srcset="https://substackcdn.com/image/fetch/$s_!-TyH!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp 424w, https://substackcdn.com/image/fetch/$s_!-TyH!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp 848w, https://substackcdn.com/image/fetch/$s_!-TyH!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp 1272w, https://substackcdn.com/image/fetch/$s_!-TyH!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa5125b76-232f-41bf-a555-bc173dfd9acd_1233x454.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div></div></div></div><figcaption class="image-caption"><a href="https://cds.cern.ch/record/405662/files/PhysRev.47.777.pdf">EPR 1935 paper</a></figcaption></figure></div><p>Call these hidden factors &#8220;hidden variables,&#8221; and the resulting theory is called a &#8220;local hidden-variable theory&#8221; (LHVT).</p><p>In 1951, the EPR paper&#8217;s thought experiment was reformulated by David Bohm. After two particles that had been bound together separated, conservation of angular momentum meant that measuring the spin value of one particle along a certain axis would reveal the spin value of the other particle along the same axis. Spin values are discrete, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\pm 1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and are easier to measure precisely in experiments than the continuous position and momentum.</p><p>In 1964, John Bell turned this thought experiment into a falsifiable inequality, allowing LHVT to be falsified using statistical values from experimental data. In 1969, John Clauser and others removed one strict condition required by Bell&#8217;s thought experiment&#8212;that measurements along the same direction on the two sides be perfectly anticorrelated, which no real source, analyzer, or detector achieves&#8212;and designed a version that was easier to test experimentally, together with a new inequality known as the CHSH inequality.</p><p>To date, Bell inequalities (CHSH and its variants) have been violated in several dozen experiments, e.g., <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.28.938">Freedman &amp; Clauser 1972</a>, <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.49.1804">Aspect et al. 1982</a>, <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.81.5039">Weihs et al. 1998</a>, <a href="https://www.nature.com/articles/nature15759">Hensen et al. 2015</a>.</p><p>These experimental results suggest that we abandon our belief in &#8220;local realism.&#8221; In its place, there exists in the universe an action-at-a-distance force that can transmit causal effects instantaneously. It is precisely this action-at-a-distance force that is responsible for state updates in quantum-entangled systems.</p><p>Recall the cellular automaton from earlier. With the particle moving at infinite speed, we could squint and view the two balls as a quantum-entangled system. When the color of one ball is measured, the color of the other ball is frozen into the same color at that very instant.</p><h2>3. Harnessing the Spooky Action</h2><h3>The CHSH Test and Inequality</h3><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!7Ova!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!7Ova!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp 424w, https://substackcdn.com/image/fetch/$s_!7Ova!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp 848w, https://substackcdn.com/image/fetch/$s_!7Ova!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp 1272w, https://substackcdn.com/image/fetch/$s_!7Ova!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!7Ova!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp" width="590" height="418.39494163424126" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:729,&quot;width&quot;:1028,&quot;resizeWidth&quot;:590,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Title, authors and abstract of the 1969 CHSH paper, &#8220;Proposed Experiment to Test Local Hidden-Variable Theories&#8221;&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Title, authors and abstract of the 1969 CHSH paper, &#8220;Proposed Experiment to Test Local Hidden-Variable Theories&#8221;" title="Title, authors and abstract of the 1969 CHSH paper, &#8220;Proposed Experiment to Test Local Hidden-Variable Theories&#8221;" srcset="https://substackcdn.com/image/fetch/$s_!7Ova!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp 424w, https://substackcdn.com/image/fetch/$s_!7Ova!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp 848w, https://substackcdn.com/image/fetch/$s_!7Ova!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp 1272w, https://substackcdn.com/image/fetch/$s_!7Ova!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F39704c6a-56d8-433e-929e-1ee8eca3da4c_1028x729.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.23.880">The CHSH test paper</a></figcaption></figure></div><p>Let&#8217;s study the CHSH inequality:</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;\\langle a_1 \\cdot b_1 \\rangle+\\langle a_1 \\cdot b_2 \\rangle+\\langle a_2 \\cdot b_1 \\rangle- \\langle a_2 \\cdot b_2 \\rangle \\leq 2&quot;,&quot;id&quot;:&quot;PQOZPABHKU&quot;}" data-component-name="LatexBlockToDOM"></div><p>Picture Alice and Bob as two experimenters separated in space. Between them is a pair of twin particles bound together. Suddenly, the pair splits apart, and each particle flies toward one of the experimenters. The experimenters are interested in the spin values of these particles, and each chooses 2 directions along which to perform measurements. For example, Alice&#8217;s first direction may be the vertical direction perpendicular to the ground, while her second direction may be parallel to the ground to her right-hand side. The two experimenters may freely choose whichever directions they prefer.</p><p>Any measured spin value of a particle can only be +1 or -1:</p><ul><li><p>+1 means &#8220;the particle was measured to spin along the measurement direction!&#8221;</p></li><li><p>-1 means &#8220;the particle was measured to spin in the direction opposite to the measurement direction!&#8221;</p></li></ul><p>Now let&#8217;s formalize our discussion with variables. Alice&#8217;s two measurement directions are <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. The spin value obtained by measuring along <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, while the spin value obtained by measuring along <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Thus,</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;a_1,a_2\\in\\{+1,-1\\}&quot;,&quot;id&quot;:&quot;VKXWYXVNBU&quot;}" data-component-name="LatexBlockToDOM"></div><p>Bob&#8217;s directions are <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and his results are</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;b_1,b_2\\in\\{+1,-1\\}&quot;,&quot;id&quot;:&quot;UVBVXIDGZT&quot;}" data-component-name="LatexBlockToDOM"></div><p>Alice and Bob perform this experiment many times, independently record their measurement results, and finally run a statistical analysis.</p><p>In each experimental run, there are only 4 possible combinations of Alice&#8217;s and Bob&#8217;s measurement directions:</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;A_1B_1,\\quad A_1B_2,\\quad A_2B_1,\\quad A_2B_2&quot;,&quot;id&quot;:&quot;ZJFVGAAKYA&quot;}" data-component-name="LatexBlockToDOM"></div><p>In each run, the <em>product</em> of Alice&#8217;s and Bob&#8217;s measurement results takes one of two possible values: <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;+1, -1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p><p>The left-hand side of the CHSH inequality is this expression:</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;\\langle a_1 \\cdot b_1 \\rangle+\\langle a_1 \\cdot b_2 \\rangle+\\langle a_2 \\cdot b_1 \\rangle- \\langle a_2 \\cdot b_2 \\rangle&quot;,&quot;id&quot;:&quot;RGCHBRJWEU&quot;}" data-component-name="LatexBlockToDOM"></div><p>where <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\langle\\ \\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> denotes the statistical average. What do these averages mean? Take <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\langle a_1\\cdot b_1\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Across all experimental runs, select those where Alice and Bob used the measurement combination <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A_1 B_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Calculate the product of their results from each selected run, then take the average.</p><p>Therefore, the above expression amounts to calculating four average values from experimental data, adding the first three together, and subtracting the fourth.</p><p>If we believe in &#8220;local realism,&#8221; after the particles separate, they no longer exchange information. Each particle carries its own &#8220;real values&#8221; toward its respective experimenter. Imagine that when the particle flying toward Bob separates from its twin, it has already &#8220;decided&#8221;: if Bob measures along direction <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, I will give him the result +1; if he measures along <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, I will give him the result -1.</p><p>By enumerating all possible &#8220;decisions&#8221; that the pair of twin particles could make, the authors of the CHSH paper found that &#8220;local realism&#8221; leads to:</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;\\langle a_1 \\cdot b_1 \\rangle+\\langle a_1 \\cdot b_2 \\rangle+\\langle a_2 \\cdot b_1 \\rangle- \\langle a_2 \\cdot b_2 \\rangle \\leq 2&quot;,&quot;id&quot;:&quot;QKQUQYSFMF&quot;}" data-component-name="LatexBlockToDOM"></div><p>However, to date, several dozen experiments have produced data that violate this inequality.</p><h3>The CHSH Game</h3><p>Some researchers are not so much interested in &#8220;local realism.&#8221; After all, they&#8212;or their academic advisors&#8212;were already persuaded by Bohr back in the days of the Solvay conferences. Their focus is on quantum information <em>technology</em>: What use does this spooky action have in information technology?</p><p>In the early 2000s, the experimental test of the CHSH inequality was reformulated as a cooperative information game:</p><ul><li><p>Alice and Bob are separated and cannot communicate.</p></li><li><p>A neutral referee gives each of them a random bit, with values <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;x&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;y&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and asks each of them to return one bit to the referee, with values <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>Alice and Bob win together:</p><ul><li><p>If <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;(x, y) = (1, 1)&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> must differ.</p></li><li><p>If <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;x&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;y&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> take any of the other 3 combinations, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> must be the same.</p></li></ul></li></ul><p>Compress the conditions above into a single equation:</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;a \\oplus b = x \\land y&quot;,&quot;id&quot;:&quot;VSTEOVFMUQ&quot;}" data-component-name="LatexBlockToDOM"></div><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!5IiC!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!5IiC!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp 424w, https://substackcdn.com/image/fetch/$s_!5IiC!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp 848w, https://substackcdn.com/image/fetch/$s_!5IiC!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp 1272w, https://substackcdn.com/image/fetch/$s_!5IiC!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!5IiC!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp" width="494" height="385.76785714285717" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/cbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1137,&quot;width&quot;:1456,&quot;resizeWidth&quot;:494,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;CHSH game diagram: a referee sends bits x and y to Alice and Bob, who reply with a and b; the referee checks whether x &#8743; y equals a &#8853; b&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="CHSH game diagram: a referee sends bits x and y to Alice and Bob, who reply with a and b; the referee checks whether x &#8743; y equals a &#8853; b" title="CHSH game diagram: a referee sends bits x and y to Alice and Bob, who reply with a and b; the referee checks whether x &#8743; y equals a &#8853; b" srcset="https://substackcdn.com/image/fetch/$s_!5IiC!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp 424w, https://substackcdn.com/image/fetch/$s_!5IiC!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp 848w, https://substackcdn.com/image/fetch/$s_!5IiC!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp 1272w, https://substackcdn.com/image/fetch/$s_!5IiC!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fcbe57c26-5809-4fc0-b9fb-57e8c3b2b7bb_2000x1562.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Image: CHSH-quantum-extra-credit, <a href="https://commons.wikimedia.org/wiki/File:Chsh-illustration.png">Wikimedia Commons</a>, <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a></figcaption></figure></div><p>Interestingly, because quantum entanglement does not count as communication, the game allows Alice and Bob to share and operate on a pair of entangled particles. Imagine the two balls from our earlier cellular automaton: Alice and Bob may each hold one of them.</p><p>How should Alice and Bob play? Consider the challenge. When <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;(x, y) = (1, 1)&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, the two must give different answers; in the other three cases, they must give the same answer. However, they have no way to communicate and determine which case they are in. Therefore, without leveraging quantum entanglement, their best strategy is very simple: before the game begins, they agree that no matter what happens, they will both return the same answer. Their winning probability is 75%. It is impossible to get any higher than that.</p><p>What if they leverage quantum entanglement? Alice and Bob can prepare a pair of entangled particles in the following state:</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;\\frac{1}{\\sqrt{2}}( |00\\rangle + |11\\rangle )&quot;,&quot;id&quot;:&quot;ECTQUQTVRX&quot;}" data-component-name="LatexBlockToDOM"></div><p>For this pair of particles, as long as both sides measure along the same direction (all the directions in this example lie in one plane), no matter who measures first or what result is obtained, the measurement outcomes on the two sides will always agree.</p><p>Alice and Bob then agree on the following strategy:</p><ul><li><p>Each chooses two measurement directions. Alice&#8217;s directions are <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A_1,A_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, while Bob&#8217;s directions are <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B_1,B_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>During the game:</p><ul><li><p>If Alice receives the random bit <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;x=0&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, she measures her entangled particle along direction <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, obtaining the result <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. If she receives <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;x=1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, she measures along direction <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, obtaining the result <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>If Bob receives <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;y=0&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, he measures along direction <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, obtaining the result <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. If he receives <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;y=1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, he measures along direction <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;B_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, obtaining the result <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li></ul></li><li><p>As in the CHSH test, any measurement result can only be +1 or -1.</p></li><li><p>Alice and Bob each submit their measurement result to the referee as their answer.</p></li></ul><p>To maximize the winning probability, what directions should <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;A_1,A_2,B_1,B_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> be?</p><p>The rules of the game tell us that when <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;x=y=1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, Alice and Bob must give different answers to win. In other words, the product <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a_2 \\cdot b_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> must be negative. Therefore, Alice and Bob are effectively trying to maximize the following statistical quantity:</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;\\langle a_1 \\cdot b_1 \\rangle + \\langle a_1 \\cdot b_2 \\rangle + \\langle a_2 \\cdot b_1 \\rangle - \\langle a_2 \\cdot b_2 \\rangle&quot;,&quot;id&quot;:&quot;QDUYMYVVAS&quot;}" data-component-name="LatexBlockToDOM"></div><p>This is exactly the left-hand side of the CHSH inequality!</p><p>Skipping the derivation&#8212;which involves wave-function basis projection, beyond the scope of this article&#8212;we find that Alice and Bob can choose the following measurement directions to maximize their winning probability:</p><ul><li><p>A1 = 0&#176;</p></li><li><p>A2 = 90&#176;</p></li><li><p>B1 = 45&#176;</p></li><li><p>B2 = -45&#176;</p></li></ul><p>These choices lead to a winning probability of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\cos^2(22.5^\\circ)\\approx 0.8536&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, or 85.36%, which is greater than the maximum winning probability of 75% when quantum entanglement is not used.</p><p>Note that Alice and Bob each measure the entangled particle in their possession. The act of measurement &#8220;consumes&#8221; the particles: after they are measured, they are no longer entangled.</p><p>This notion of consumption suggests that entangled particles can be considered as an engineering resource to perform nonlocal operations on quantum states.</p><h3>Quantum Teleportation Circuit</h3><p>A more generalized goal than winning the CHSH game is: how to transfer a piece of quantum information from Alice in one location to Bob in another location using entangled particles?</p><p>To clarify, even with quantum entanglement, we cannot achieve faster-than-light transmission of classical information. However, by consuming a pair of entangled particles, we can transfer the quantum state held by Alice to Bob. Notice that after the transfer, Alice no longer possesses the quantum state, as we are confined by the no-cloning theorem.</p><p>At a basic level, the transfer involves 5 steps:</p><ol><li><p>Prepare a pair of entangled particles, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, in the so-called Bell state. The measurement results on these two particles are either both 0 or both 1, with equal probability.</p></li></ol><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;\\frac{1}{\\sqrt{2}}(|00\\rangle+|11\\rangle)&quot;,&quot;id&quot;:&quot;BXTBYKWZSL&quot;}" data-component-name="LatexBlockToDOM"></div><ol start="2"><li><p>Distribute <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> to Alice, and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> to Bob, while keeping <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> entangled.</p></li><li><p>Alice entangles her particle with the message quantum state <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;m&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. At this point, the three quantum states <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;m&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> are all entangled together.</p></li><li><p>Alice measures <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;m&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, thereby consuming <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> as a resource, and collapsing <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;m&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>Alice communicates the measurement results&#8212;classical information&#8212;to Bob through a classical communication channel. Based on the information received, Bob performs the corresponding quantum gate operations on <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> as a correction. Now, Bob possesses the message quantum state <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;m&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li></ol><p>The entire process can be represented by the following quantum circuit. Quantum gate symbols such as the <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;H&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> gate and the <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;X&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Z&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> gates are beyond the scope of this article; the <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\oplus&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> symbol representing the CNOT gate will be explained below.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!FL40!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!FL40!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp 424w, https://substackcdn.com/image/fetch/$s_!FL40!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp 848w, https://substackcdn.com/image/fetch/$s_!FL40!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp 1272w, https://substackcdn.com/image/fetch/$s_!FL40!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!FL40!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp" width="1456" height="931" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/baf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:931,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Quantum teleportation circuit: an entangled pair a and b is prepared and split between Alice and Bob; Alice entangles the message m with a and measures both; Bob applies X and Z gates according to the results and ends up holding m&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Quantum teleportation circuit: an entangled pair a and b is prepared and split between Alice and Bob; Alice entangles the message m with a and measures both; Bob applies X and Z gates according to the results and ends up holding m" title="Quantum teleportation circuit: an entangled pair a and b is prepared and split between Alice and Bob; Alice entangles the message m with a and measures both; Bob applies X and Z gates according to the results and ends up holding m" srcset="https://substackcdn.com/image/fetch/$s_!FL40!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp 424w, https://substackcdn.com/image/fetch/$s_!FL40!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp 848w, https://substackcdn.com/image/fetch/$s_!FL40!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp 1272w, https://substackcdn.com/image/fetch/$s_!FL40!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fbaf790a0-ca25-4841-8d00-fc0d8d1345a1_1459x933.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><h3>Scaling Challenges of Quantum Computing</h3><p>In scaling quantum computers, one of the most basic metrics is the physical qubit count: the number of physical qubits that a computing platform can prepare, maintain, and operate at the physical level.</p><p>Over the past thirty years, the number of qubits on a single (monolithic) platform has continued to increase. In recent years, neutral-atom platforms in particular have scaled at the fastest rate, as shown in the figure below.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!tX5d!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!tX5d!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp 424w, https://substackcdn.com/image/fetch/$s_!tX5d!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp 848w, https://substackcdn.com/image/fetch/$s_!tX5d!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp 1272w, https://substackcdn.com/image/fetch/$s_!tX5d!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!tX5d!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp" width="850" height="680" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/fd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:680,&quot;width&quot;:850,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Chart of physical qubit counts by platform from 1998 to 2024 on a log scale; neutral atoms grow fastest, doubling about every 1.4 years&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Chart of physical qubit counts by platform from 1998 to 2024 on a log scale; neutral atoms grow fastest, doubling about every 1.4 years" title="Chart of physical qubit counts by platform from 1998 to 2024 on a log scale; neutral atoms grow fastest, doubling about every 1.4 years" srcset="https://substackcdn.com/image/fetch/$s_!tX5d!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp 424w, https://substackcdn.com/image/fetch/$s_!tX5d!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp 848w, https://substackcdn.com/image/fetch/$s_!tX5d!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp 1272w, https://substackcdn.com/image/fetch/$s_!tX5d!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd7a3c0e-f807-4bcc-8454-1813faaf3eec_850x680.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Source: <em><a href="https://arxiv.org/abs/2507.03678">Awesome Quantum Computing Experiments</a></em> (Le R&#233;gent 2025)</figcaption></figure></div><p>However, if we require that the physical qubits be flexibly allocatable to perform 1-qubit gates and 2-qubit gates, the limit today is in the hundreds of physical qubits on a single platform. For example:</p><ul><li><p>256 qubits in <em><a href="https://arxiv.org/html/2411.11822v1">Logical computation demonstrated with a neutral atom quantum processor</a></em>.</p></li><li><p>280 qubits in <em><a href="https://www.nature.com/articles/s41586-023-06927-3">Logical quantum processor based on reconfigurable atom arrays</a></em>.</p></li></ul><p>Across different qubit types, single-platform scaling encounters various difficulties.</p><h4>Superconducting-Circuit Platforms</h4><p><em>Superconducting-circuit</em> platforms operate superconducting circuits at low temperatures as qubits, and use the two lowest energy levels of the circuit as <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|0\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|1\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. The energy gap is commonly around 20 &#181;eV, corresponding to an excitation frequency of approximately 5 GHz. Therefore, transitions between the two energy levels rely on 5 GHz microwave signals.</p><p>However, a 5 GHz signal corresponds to a wavelength of approximately 3 centimeters in a waveguide, which is on par with the scale of the entire circuit system, leading to significant crosstalk: a signal originally intended to drive a specific qubit spills over and affects other qubits. In practice, excitation frequencies of neighboring qubits are staggered through deliberate control of circuit dimensions. However, one limitation of this design is that if qubits A and B are adjacent, and A&#8217;s excitation frequency is lower than B&#8217;s, then A&#8217;s <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|0\\rangle \\leftrightarrow |1\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> frequency may be close to B&#8217;s <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|1\\rangle\\leftrightarrow|2\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> frequency. As a result, when the signal driving A spills over to B, it may push B into <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|2\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, causing information loss. This limits the number of excitation frequencies that can be accommodated within finite bandwidth.</p><p>Moreover, the entire superconducting circuit system typically operates at approximately 0.015 K and must be placed inside a specially designed refrigerator. More qubits require more control signal lines and readout signal lines to be routed into the refrigerator, bringing in more heat and increasing noise. Noise destroys quantum states.</p><h4>Trapped-Ion Platforms</h4><p><em>Trapped-ion</em> platforms cool ions to low temperatures using methods such as Doppler cooling and sideband cooling, and confine them in potential wells formed by alternating electric fields (Paul traps, e.g., <a href="https://www.fuw.edu.pl/~szczytko/NT/materialy/9_QC/Cirac_Zoller_PRL1995.pdf">Cirac &amp; Zoller 1995</a> and <a href="https://tf.nist.gov/general/pdf/140.pdf">Monroe et al. 1995</a>) or by a static electric field combined with a strong magnetic field (Penning traps, e.g., <a href="https://arxiv.org/abs/1812.06755">Jain et al. 2018</a>). Each ion constitutes an individual qubit. In addition to their individual quantum states, these qubits form collective vibrational modes within the shared electromagnetic field. By coupling their quantum states to these collective vibrational modes, the qubits can become entangled for the purpose of performing 2-qubit gate operations.</p><p>However, once the number of qubits increases, the collective vibrational modes become more complex, and the modes crowd together, making unintended entanglement more likely and causing errors in computation. Therefore, researchers moved on from building one large trap shared by all qubits to building multiple independent smaller traps. This approach requires the ability to transport ions between traps, increasing architectural complexity. The transport process also generates noise that interferes with the quantum states.</p><h4>Neutral-Atom Platforms</h4><p><em>Neutral-atom</em> platforms cool neutral atoms to low temperatures using methods such as magneto-optical trapping and sideband cooling. Each atom is confined by an optical tweezer at a specific position, forming a matrix of qubits.</p><p>Increasing the number of qubits requires scaling up the optical systems that control them: these systems must simultaneously operate large numbers of optical tweezers and laser beams for excitation and readout, while maintaining high precision in frequency, phase, and spatial positioning.</p><p>After cooling is completed, the neutral atoms must be rearranged into a matrix with optical tweezers. The more qubits there are, the longer the rearrangement takes and the farther the atoms must be transported, increasing noise.</p><p>To create quantum entanglement, neutral atoms are excited into highly excited Rydberg states. Through van der Waals forces, an atom in a Rydberg state suppresses the probability of nearby atoms getting excited to the same state, a mechanism known as the Rydberg blockade, which causes neighboring atoms to become entangled. However, as the number and density of qubits increase, van der Waals forces are more likely to affect nearby atoms that should not be affected, causing gate errors.</p><p>If we scale up the number of qubits without increasing density, the overall array becomes larger, increasing the distance and time required for rearrangement and atom transport, thereby increasing noise.</p><h3>Quantum Supercomputer</h3><p>Consider the evolution of classical computers. Because complex scientific simulation problems exceeded the capabilities of any single machine, massively parallel processing emerged in the 1980s and 1990s. Supercomputers such as those built by Cray at the time connected as many as two thousand processors together.</p><p>Quantum computing today remains at a very early stage: no single quantum machine has yet provided commercial application value that classical computers cannot provide. To accelerate scaling, researchers began to ask: as with classical supercomputers, how can we connect multiple small quantum platforms to build a quantum supercomputer?</p><p>This mission involves challenges that do not exist in classical supercomputers: quantum states <a href="https://en.wikipedia.org/wiki/No-cloning_theorem">cannot be copied</a>, and physical transportation exposes them to noise and decoherence. Ideally, multiple quantum platforms would share quantum states and operate on those states while avoiding the physical movement of qubits as much as possible. This would allow multiple quantum platforms to be &#8220;virtualized&#8221; into a single ultra-large platform with effectively a great number of qubits to unlock new computational problems beyond the capabilities of any classical computer.</p><h3>Nonlocal Gates</h3><p>One of the keys lies in harnessing the spooky action to build <em>nonlocal gates</em>.</p><p>Consider a classical computer. A logic gate occupies a specific location and area on a chip. Through the materials used in the gate, its structural design, and other factors, the gate maintains the intended logical relationship between its input and output signals. For example, if we want to perform an XOR operation <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\oplus&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> on two classical bits, we must transmit the signals carrying those two bits to the input ports of a single XOR circuit, positioned at a particular locality in the circuit system, and capture the result at its output port.</p><p>A nonlocal gate, in contrast, can perform a logical operation on multiple input data located in different places, despite the distance between them. Imagine in Laboratory 101 a quantum platform contains a qubit <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> in quantum state <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;x&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, while in the neighboring Laboratory 102 a quantum platform contains a qubit <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> in quantum state <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;y&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Through a nonlocal gate, without moving either <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> or <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, we can &#8220;snap our fingers&#8221; from afar and make the quantum state of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> become <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;x\\oplus y&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, at the cost of one pre-shared entangled pair and one classical bit sent in each direction.</p><p>Let&#8217;s study the Remote CNOT described in <a href="https://arxiv.org/pdf/quant-ph/0005101">Eisert et al. 2000</a>.</p><p>CNOT, or controlled-NOT, is a 2-qubit gate. It has two inputs, <code>control in</code> and <code>target in</code>, and two outputs, <code>control out</code> and <code>target out</code>. Its rule is simple: when <code>control in</code> is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|1\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, <code>target in</code> is flipped (more precisely, an <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;X&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> gate is applied) to produce <code>target out</code>; otherwise, <code>target out</code> is equal to <code>target in</code>. CNOT is one of the most basic logic gates and is included in the universal gate sets of many computing platforms.</p><p>A regular CNOT operates on two qubits that are adjacent in physical space&#8212;that is, local. A Remote CNOT goes beyond locality:</p><ul><li><p>Alice and Bob are separated and each hold one qubit, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>In addition, Alice and Bob each hold one qubit of an entangled qubit pair, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>Through the Remote CNOT, Alice and Bob can perform CNOT(<span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>), using <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> as the control and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> as the target. If <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|0\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> remains unchanged; if <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|1\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is flipped.</p></li></ul><p>Consider the circuit:</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!HtdH!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!HtdH!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp 424w, https://substackcdn.com/image/fetch/$s_!HtdH!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp 848w, https://substackcdn.com/image/fetch/$s_!HtdH!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp 1272w, https://substackcdn.com/image/fetch/$s_!HtdH!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!HtdH!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp" width="1456" height="774" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:774,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Remote CNOT circuit: Alice and Bob each hold one qubit of an entangled pair; after six steps and one classical message in each direction, Bob&#8217;s qubit becomes a &#8853; b&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Remote CNOT circuit: Alice and Bob each hold one qubit of an entangled pair; after six steps and one classical message in each direction, Bob&#8217;s qubit becomes a &#8853; b" title="Remote CNOT circuit: Alice and Bob each hold one qubit of an entangled pair; after six steps and one classical message in each direction, Bob&#8217;s qubit becomes a &#8853; b" srcset="https://substackcdn.com/image/fetch/$s_!HtdH!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp 424w, https://substackcdn.com/image/fetch/$s_!HtdH!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp 848w, https://substackcdn.com/image/fetch/$s_!HtdH!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp 1272w, https://substackcdn.com/image/fetch/$s_!HtdH!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F736f9969-c4b9-48cc-bf09-c7da2549c306_1744x927.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>The entire procedure consists of 6 steps:</p><ol><li><p>Prepare an entangled pair in the Bell state, with the two qubits denoted as <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li></ol><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;\\frac{1}{\\sqrt{2}}(|00\\rangle+|11\\rangle)&quot;,&quot;id&quot;:&quot;IHXCNYXJFV&quot;}" data-component-name="LatexBlockToDOM"></div><ol start="2"><li><p>&#8220;Distribute&#8221; <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> to Alice and Bob, respectively. How to &#8220;distribute&#8221; without physically transporting the qubits will be discussed below.</p></li><li><p>Alice entangles her qubit <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> with <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>Alice measures <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, thereby consuming it, and communicates the measurement result to Bob through a classical channel. Bob then uses that information as the control bit to run a CNOT on <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, a local correction.</p></li><li><p>Bob entangles his qubit <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> with <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>Bob measures <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, thereby consuming it, and communicates the measurement result to Alice through a classical channel. Alice then uses that information as the control bit to run a CZ (controlled-Z) operation on <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, a local correction.</p></li></ol><p>After these steps, the qubits held by Alice and Bob have undergone a joint state transformation equivalent to that of a local CNOT:</p><div class="latex-rendered" data-attrs="{&quot;persistentExpression&quot;:&quot;|a\\rangle|b\\rangle\\longmapsto |a\\rangle|a\\oplus b\\rangle&quot;,&quot;id&quot;:&quot;OAUMKKENDA&quot;}" data-component-name="LatexBlockToDOM"></div><p>The resources consumed by this procedure are:</p><ul><li><p>1 <em>ebit</em> of shared entanglement</p></li><li><p>1 <em>cbit</em> of classical communication in each direction</p></li></ul><p>Overall, pre-shared entanglement is a consumable resource. By consuming entanglement, exchanging classical measurement results, and applying local correction operations, we can have two spatially separated qubits jointly execute a logic gate without physically transporting either qubit.</p><h2>4. Commercial Ambition</h2><h3>Entanglement Swapping</h3><p>For both the quantum teleportation circuit and the nonlocal gate, steps 1 and 2 are &#8220;prepare an entangled qubit pair; distribute the entangled qubits to the two parties.&#8221; The question is: how do we distribute the entangled qubits without physically transporting them?</p><p>In fact, we do not distribute the qubits. It is not the case that <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> are prepared somewhere and then distributed to Alice and Bob.</p><p>The practical approach is to use photons as &#8220;flying qubits&#8221; to transform a pair of qubits already held by Alice and Bob into an entangled state.</p><p>More specifically, neutral-atom and trapped-ion platforms prepare entanglement resources in the following way:</p><ol><li><p>Alice and Bob each allocate one qubit, denoted as <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, to be transformed into an entanglement resource.</p></li><li><p>Repeat the following steps until success:</p><ol><li><p>Alice and Bob each excite the qubit in their possession, causing it to emit a photon, denoted as <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;p_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;p_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. The qubit&#8211;photon pair <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a - p_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is entangled, and the pair <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b - p_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> is also entangled. The specific method of excitation will be discussed below.</p></li><li><p>For either party, after successful entanglement, the state of the qubit&#8211;photon pair can be described by the following expression: <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\frac{1}{\\sqrt{2}} \\left( |0\\rangle_e|H\\rangle_p + |1\\rangle_e|V\\rangle_p \\right)&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. This means that there is a 1/2 probability of measuring &#8220;qubit in 0, photon in horizontal polarization,&#8221; and a 1/2 probability of measuring &#8220;qubit in 1, photon in vertical polarization.&#8221;</p></li><li><p>Send the two photons <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;p_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;p_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> to an interference station. Here, we perform interference with the two photons so that the spatially separated qubits <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> become entangled. This involves 2 steps:</p><ol><li><p>Send the 2 photons into a beam splitter with 2 inputs and 2 outputs. Our goal is to &#8220;mix&#8221; them so that the 2 output photons cannot be individually traced back to their corresponding input photons. Functionally, this is analogous to a <a href="https://en.wikipedia.org/wiki/Cryptocurrency_tumbler">cryptocurrency mixer</a>. If successful, the 2 photons can be treated as a joint system.</p></li><li><p>Measure the polarization directions of the 2 photons. This measurement procedure is called a Bell-state measurement (BSM). When the measurement result shows one of the specific combinations of polarization directions, we can declare, or <em>herald</em>, that <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> have successfully entered an entangled state. If we fail to see the specific combinations in our BSM result, we return to step 2a and repeat until this step succeeds.</p></li></ol></li></ol></li></ol><p>This procedure transforms two qubit&#8211;photon entanglement pairs, <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a - p_a&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_b - p_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, into one qubit&#8211;qubit entanglement pair <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;e_a - e_b&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. Proposed in 1993, this procedure is called entanglement swapping.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!8GR6!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!8GR6!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp 424w, https://substackcdn.com/image/fetch/$s_!8GR6!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp 848w, https://substackcdn.com/image/fetch/$s_!8GR6!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp 1272w, https://substackcdn.com/image/fetch/$s_!8GR6!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!8GR6!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp" width="1403" height="557" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/f9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:557,&quot;width&quot;:1403,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Title and abstract of the 1993 paper &#8220;&#8216;Event-Ready-Detectors&#8217; Bell Experiment via Entanglement Swapping&#8221;&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Title and abstract of the 1993 paper &#8220;&#8216;Event-Ready-Detectors&#8217; Bell Experiment via Entanglement Swapping&#8221;" title="Title and abstract of the 1993 paper &#8220;&#8216;Event-Ready-Detectors&#8217; Bell Experiment via Entanglement Swapping&#8221;" srcset="https://substackcdn.com/image/fetch/$s_!8GR6!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp 424w, https://substackcdn.com/image/fetch/$s_!8GR6!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp 848w, https://substackcdn.com/image/fetch/$s_!8GR6!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp 1272w, https://substackcdn.com/image/fetch/$s_!8GR6!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ff9e4e8ba-d8ac-4b18-8497-b1a3a777ad70_1403x557.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.71.4287">The entanglement-swapping paper</a></figcaption></figure></div><p>We are still missing a piece of the puzzle: in step 2a, how is the qubit&#8211;photon entanglement generated?</p><h3>Qubit&#8211;Photon Interface</h3><p>How can a qubit <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> be &#8220;excited&#8221; so that the photon <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;P&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> it emits becomes entangled with <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>?</p><p>Consider a neutral-atom or trapped-ion qubit <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> in free space. A laser pulse excites <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, which then decays and emits a photon <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;P&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. If the excited <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> has multiple decay paths available, the energy level of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> after emission and the state of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;P&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, such as its polarization direction, may become entangled.</p><p>However, carrying out this process in free space involves at least the following 3 variables:</p><ol><li><p>To which energy level will the excited <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> decay, and what frequency will <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;P&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> have?</p></li><li><p>In which direction will the excited <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> emit <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;P&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>?</p></li><li><p>How much time will pass between excitation and emission?</p></li></ol><p>For Variable 1, we want <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> to return to either <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|0\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> or <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|1\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> after emission. Any quantum platform, using neutral atoms or ions of a particular element under a particular external magnetic field, defines its particular <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\{ |0\\rangle, |1\\rangle \\}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> as its computational subspace. For classical computing, the &#8220;computational subspace&#8221; is the pair of voltage levels {0 V, 1.2 V} on a CMOS chip, interpreted as logical 0 and logical 1, respectively. If <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> ends up outside <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\{ |0\\rangle, |1\\rangle \\}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> after emission, this constitutes a leakage from the computational subspace. If the leakage cannot be corrected, we lose quantum information.</p><p>For Variable 2, radiation in free space may be carried out randomly in many different directions. When the direction is uncontrollable, we have low efficiency in photon collection.</p><p>For Variable 3, the emission time in free space is also random. More specifically, the waiting time until decay follows an exponential distribution. A cavity, by contrast, can shorten and shape the photon&#8217;s wave packet, making it easier for the photons from Alice and Bob to overlap at the beam splitter and allowing a higher repetition rate.</p><p>To make the decay path, emission direction, and timing more controllable, researchers use <em>cavities</em> to alter the electromagnetic environment surrounding the qubits. This is an application of the Purcell effect. In 1946, Edward Purcell, while studying nuclear magnetic resonance, proposed in a brief conference abstract that if an emitter is placed inside a cavity and the cavity&#8217;s mode resonates with the emission transition, the rate of emission is enhanced. This cavity-induced modification of the spontaneous-emission rate is known as the Purcell effect.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!OtaK!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!OtaK!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp 424w, https://substackcdn.com/image/fetch/$s_!OtaK!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp 848w, https://substackcdn.com/image/fetch/$s_!OtaK!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp 1272w, https://substackcdn.com/image/fetch/$s_!OtaK!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!OtaK!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp" width="532" height="567.4666666666667" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1120,&quot;width&quot;:1050,&quot;resizeWidth&quot;:532,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Purcell&#8217;s 1946 conference abstract, &#8220;Spontaneous Emission Probabilities at Radio Frequencies&#8221;&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Purcell&#8217;s 1946 conference abstract, &#8220;Spontaneous Emission Probabilities at Radio Frequencies&#8221;" title="Purcell&#8217;s 1946 conference abstract, &#8220;Spontaneous Emission Probabilities at Radio Frequencies&#8221;" srcset="https://substackcdn.com/image/fetch/$s_!OtaK!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp 424w, https://substackcdn.com/image/fetch/$s_!OtaK!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp 848w, https://substackcdn.com/image/fetch/$s_!OtaK!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp 1272w, https://substackcdn.com/image/fetch/$s_!OtaK!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F21f3d392-6745-446c-b8ef-d3392bd54ef7_1050x1120.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><a href="https://chemphys.ca/pbunker/Purcell.pdf">1946 conference abstract by Purcell</a></figcaption></figure></div><p>By constructing the cavity from two opposing mirrors and carefully designing the cavity geometry and qubit placement, we can better control the decay path, direction, and timing of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;Q&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>&#8217;s emission. If one mirror is made slightly more transmissive, it can serve as the &#8220;egress,&#8221; allowing <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;P&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> to leave the cavity, enter an optical fiber, and travel to the interference station. <a href="https://www.science.org/cms/asset/c072530d-7c3d-471f-bf61-6c0f020af8d8/pap.pdf">Wilk et al. 2007</a> is one of the early representative works that realized such a design.</p><div class="captioned-image-container"><figure><div class="image-link image2" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!_iRP!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp 424w, https://substackcdn.com/image/fetch/$s_!_iRP!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp 848w, https://substackcdn.com/image/fetch/$s_!_iRP!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp 1272w, https://substackcdn.com/image/fetch/$s_!_iRP!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!_iRP!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp" width="391" height="234.43254817987153" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/fbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:280,&quot;width&quot;:467,&quot;resizeWidth&quot;:391,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Diagram: an atom inside a cavity formed by two mirrors is excited by laser pulses, and a photon leaves through one of the mirrors&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Diagram: an atom inside a cavity formed by two mirrors is excited by laser pulses, and a photon leaves through one of the mirrors" title="Diagram: an atom inside a cavity formed by two mirrors is excited by laser pulses, and a photon leaves through one of the mirrors" srcset="https://substackcdn.com/image/fetch/$s_!_iRP!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp 424w, https://substackcdn.com/image/fetch/$s_!_iRP!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp 848w, https://substackcdn.com/image/fetch/$s_!_iRP!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp 1272w, https://substackcdn.com/image/fetch/$s_!_iRP!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffbf110e9-c71b-465b-95f3-4d7bf6bda671_467x280.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div></div></div></div><figcaption class="image-caption">From <a href="https://www.science.org/cms/asset/c072530d-7c3d-471f-bf61-6c0f020af8d8/pap.pdf">Wilk et al. 2007</a></figcaption></figure></div><h3>The Ambition of Nu Quantum: Datacenter-Scale Distributed Quantum Computing</h3><p><a href="https://www.nu-quantum.com/">Nu Quantum</a> is a British company spun out of the Cambridge Cavendish Laboratory in 2018. It aims to become the &#8220;Cisco&#8221; of quantum datacenters in the future by providing networking solutions that connect quantum computers and realize distributed fault-tolerant quantum computing.</p><p>Nu Quantum uses cavities as qubit&#8211;photon interfaces (QPIs). The figure below comes from Nu Quantum&#8217;s PCT patent application WO2023073379A1; a UK patent in the same family, GB2612578B, was granted in 2024.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!licj!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!licj!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp 424w, https://substackcdn.com/image/fetch/$s_!licj!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp 848w, https://substackcdn.com/image/fetch/$s_!licj!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp 1272w, https://substackcdn.com/image/fetch/$s_!licj!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!licj!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp" width="481" height="277" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:277,&quot;width&quot;:481,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Nu Quantum patent drawing FIG. 8B: mirrors 104a and 104b form cavity 106 around qubit 112, with the excitation laser entering from the side, plus actuator 114 and mirrors 102 and 108&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Nu Quantum patent drawing FIG. 8B: mirrors 104a and 104b form cavity 106 around qubit 112, with the excitation laser entering from the side, plus actuator 114 and mirrors 102 and 108" title="Nu Quantum patent drawing FIG. 8B: mirrors 104a and 104b form cavity 106 around qubit 112, with the excitation laser entering from the side, plus actuator 114 and mirrors 102 and 108" srcset="https://substackcdn.com/image/fetch/$s_!licj!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp 424w, https://substackcdn.com/image/fetch/$s_!licj!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp 848w, https://substackcdn.com/image/fetch/$s_!licj!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp 1272w, https://substackcdn.com/image/fetch/$s_!licj!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F32cbbf3c-1c0b-4290-ad4e-27729e886eb9_481x277.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Source: Nu Quantum patent application <a href="https://patents.google.com/patent/WO2023073379A1/en">WO2023073379A1</a></figcaption></figure></div><p>A walkthrough of the main components in the design:</p><ul><li><p>104a and 104b are the two mirrors that form the cavity.</p></li><li><p>112 is the qubit.</p></li><li><p>106 is the cavity itself, the gap between 104a and 104b; the laser pulse that excites the qubit enters from the side, along the dashed arrow on the right.</p></li><li><p>114 on the left is a mechanical actuator. Using <a href="https://en.wikipedia.org/wiki/Pound%E2%80%93Drever%E2%80%93Hall_technique">Pound&#8211;Drever&#8211;Hall</a> frequency stabilization, together with mirrors 102 and 108 (rigid extensions of the cavity mirrors 104a and 104b), the distance between the mirrors is dynamically locked, which maintains the stability of the cavity-mode frequency.</p></li></ul><p>According to a <a href="https://opg.optica.org/abstract.cfm?uri=QUANTUM-2025-QM4B.2">paper</a> published by the team in 2025, the cavity is approximately 370 &#181;m long, with a waist of approximately 5 &#181;m. A 2024 press release further stated that the cavity length could be locked to within 0.08 nm. For the 780 nm transition commonly used with rubidium-87 neutral-atom qubits, this corresponds to a frequency error of approximately <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;2\\times10^{-5}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>% (about 80 MHz).</p><p><a href="https://arxiv.org/abs/2404.16167">O&#8217;Reilly et al. 2024</a>, from Monroe&#8217;s group, represents the state of the art, achieving a successful entanglement generation rate of 250 events per second, or 250 Hz. Because quantum supercomputers will require large amounts of entanglement resources, under continuous replenishment, to perform nonlocal gates, the entanglement generation rate is critical. One of Nu Quantum&#8217;s near-term goals is to increase this rate by another 2 orders of magnitude.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!mmo9!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!mmo9!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp 424w, https://substackcdn.com/image/fetch/$s_!mmo9!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp 848w, https://substackcdn.com/image/fetch/$s_!mmo9!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp 1272w, https://substackcdn.com/image/fetch/$s_!mmo9!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!mmo9!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp" width="1200" height="665" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:665,&quot;width&quot;:1200,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Nu Quantum slide of system-level targets: a 100x improvement on today&#8217;s state of the art (Monroe, 0.25 kHz), reaching an entanglement rate of 25 kHz in Gen 2 and Gen 3&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Nu Quantum slide of system-level targets: a 100x improvement on today&#8217;s state of the art (Monroe, 0.25 kHz), reaching an entanglement rate of 25 kHz in Gen 2 and Gen 3" title="Nu Quantum slide of system-level targets: a 100x improvement on today&#8217;s state of the art (Monroe, 0.25 kHz), reaching an entanglement rate of 25 kHz in Gen 2 and Gen 3" srcset="https://substackcdn.com/image/fetch/$s_!mmo9!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp 424w, https://substackcdn.com/image/fetch/$s_!mmo9!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp 848w, https://substackcdn.com/image/fetch/$s_!mmo9!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp 1272w, https://substackcdn.com/image/fetch/$s_!mmo9!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87ddf6db-1141-4e50-8c29-838df0e4ba46_1200x665.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Source: Nu Quantum CEO Carmen Palacios-Berraquero, <a href="https://www.youtube.com/watch?v=buSit-PcUJI">talk at Q2B24 Silicon Valley</a></figcaption></figure></div><p>Nu Quantum&#8217;s broader goal is to virtualize multiple quantum platforms&#8212;also known as quantum processing units, or QPUs&#8212;under the roof of a single datacenter as one distributed platform. At present, their networking solution supports only trapped-ion and neutral-atom platforms. The solution involves 3 layers:</p><ol><li><p>The QPI forms the lowest layer. Installed within each quantum platform, it generates the qubit&#8211;photon entanglement described above and outputs photons.</p></li><li><p>The next layer is the Quantum Networking Unit, or QNU. It routes and pairs photons arriving from different QPIs, repeatedly performs Bell-state measurements until successful heralding, and creates shared nonlocal entanglement resources between arbitrary pairs of QPUs.</p></li><li><p>The upper layer is Distributed Quantum Error Correction, or DQEC (refer to their <a href="https://arxiv.org/abs/2501.14029">2025 paper</a>). It performs error detection and correction across multiple QPUs, allowing the physical qubits distributed among them to be abstracted into functional logical qubits to be used by quantum software.</p></li></ol><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!WDu-!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!WDu-!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp 424w, https://substackcdn.com/image/fetch/$s_!WDu-!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp 848w, https://substackcdn.com/image/fetch/$s_!WDu-!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp 1272w, https://substackcdn.com/image/fetch/$s_!WDu-!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!WDu-!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp" width="1182" height="496" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:496,&quot;width&quot;:1182,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Nu Quantum slide mapping the classical datacenter network stack (network interface card, router, distributed computing services) onto QPI, QNU, and DQEC&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Nu Quantum slide mapping the classical datacenter network stack (network interface card, router, distributed computing services) onto QPI, QNU, and DQEC" title="Nu Quantum slide mapping the classical datacenter network stack (network interface card, router, distributed computing services) onto QPI, QNU, and DQEC" srcset="https://substackcdn.com/image/fetch/$s_!WDu-!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp 424w, https://substackcdn.com/image/fetch/$s_!WDu-!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp 848w, https://substackcdn.com/image/fetch/$s_!WDu-!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp 1272w, https://substackcdn.com/image/fetch/$s_!WDu-!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F05af5af2-7556-4c93-8f29-9dfe2eec3d43_1182x496.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Source: Nu Quantum VP Claire Le Gall, <a href="https://www.youtube.com/watch?v=_G--2n0n2Ng">talk at Q2B25 Tokyo</a></figcaption></figure></div><h3>The Ambition of CavilinQ: High-Rate Quantum Interconnects</h3><p><a href="https://www.cavilinq.com/">CavilinQ</a>, founded in 2025, shares the long-term vision of joining many separate quantum computers into one far larger machine through photonic links. CavilinQ is focusing on raising the bar on the rate and fidelity of QPIs so that photons from separate processors can be interfered and the distant qubits entangled with a higher interconnecting bandwidth.</p><p>The crux of the QPI is the interface between a qubit and the photon it emits. CavilinQ builds cavity-based interfaces that make this emission fast, directional, and well-timed, making the subsequent heralding step faster and more reliable. The team has integrated more than 5 different types of cavities with quantum memories, a hands-on experience that is rare in the field and central to making interconnects work in practice.</p><p>Recall that in a QPI, the cavity&#8217;s resonant-mode frequency must be brought as close as possible to the decay transition of the qubit. The closer the two frequencies are, the greater the probability of inducing the qubit to undergo the desired decay. One key metric is the cavity <em>finesse</em>, a dimensionless ratio. Raising the finesse (lowering the losses inside the cavity) and shrinking the beam waist strengthen the coupling between the qubit and the cavity mode, so that more photons go into the cavity mode and then out through the egress mirror.</p><p>A <a href="https://arxiv.org/abs/2509.23576">recent paper</a> by its team presents a new cavity fabrication process that achieves a finesse of about 0.9 million at a wavelength of 780 nm. A brief description of that fabrication process is as follows:</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!Y8WD!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!Y8WD!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp 424w, https://substackcdn.com/image/fetch/$s_!Y8WD!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp 848w, https://substackcdn.com/image/fetch/$s_!Y8WD!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp 1272w, https://substackcdn.com/image/fetch/$s_!Y8WD!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!Y8WD!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp" width="1207" height="393" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:393,&quot;width&quot;:1207,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;(a) The six fabrication steps: sample, wet oxide, remove oxide, coating, lithography, deep etch; (b) micrographs of the finished concave mirrors&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="(a) The six fabrication steps: sample, wet oxide, remove oxide, coating, lithography, deep etch; (b) micrographs of the finished concave mirrors" title="(a) The six fabrication steps: sample, wet oxide, remove oxide, coating, lithography, deep etch; (b) micrographs of the finished concave mirrors" srcset="https://substackcdn.com/image/fetch/$s_!Y8WD!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp 424w, https://substackcdn.com/image/fetch/$s_!Y8WD!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp 848w, https://substackcdn.com/image/fetch/$s_!Y8WD!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp 1272w, https://substackcdn.com/image/fetch/$s_!Y8WD!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F216d2a7d-3461-41a8-8f8c-ea8856eae012_1207x393.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">From <a href="https://arxiv.org/abs/2509.23576">Ding et al. 2025</a></figcaption></figure></div><ol><li><p>Smooth the surface of a silicon wafer.</p></li><li><p>Use ion-beam sputtering to deposit a coating on one side of the silicon wafer. The coating consists of dozens of alternating layers of high- and low-refractive-index materials, creating high reflectivity within the target frequency range.</p></li><li><p>Flip the silicon wafer over, apply photoresist, and perform silicon etching. The silicon substrate beneath the openings in the photoresist pattern is etched through, exposing the back side of the coating. As a result, the coating becomes suspended, and its internal stress causes it to bend into a concave mirror.</p></li><li><p>Remove the photoresist. The individual mirror chips were already released from the wafer by the through-etch in step 3, so no dicing is needed. Bond two concave mirrors facing each other to form a cavity.</p></li></ol><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!xAQI!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!xAQI!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp 424w, https://substackcdn.com/image/fetch/$s_!xAQI!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp 848w, https://substackcdn.com/image/fetch/$s_!xAQI!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp 1272w, https://substackcdn.com/image/fetch/$s_!xAQI!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!xAQI!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp" width="590" height="436" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/c80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:436,&quot;width&quot;:590,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Photo of a millimeter-scale cavity attached to an optical fiber, with an inset of two cavities on a fingertip&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Photo of a millimeter-scale cavity attached to an optical fiber, with an inset of two cavities on a fingertip" title="Photo of a millimeter-scale cavity attached to an optical fiber, with an inset of two cavities on a fingertip" srcset="https://substackcdn.com/image/fetch/$s_!xAQI!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp 424w, https://substackcdn.com/image/fetch/$s_!xAQI!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp 848w, https://substackcdn.com/image/fetch/$s_!xAQI!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp 1272w, https://substackcdn.com/image/fetch/$s_!xAQI!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc80093ae-3aa6-4b9c-9388-248142e2dbe8_590x436.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">From <a href="https://arxiv.org/abs/2509.23576">Ding et al. 2025</a></figcaption></figure></div><p>Beyond scaling quantum computing, the team is interested in the following applications:</p><h4>Blind Quantum Computing</h4><p>The concept of blind quantum computing (BQC) was proposed as early as 2001 (Childs, <em><a href="https://arxiv.org/abs/quant-ph/0111046">Secure assisted quantum computation</a></em>, published in 2005). Its defining property is <em>blindness</em>: the server learns nothing about the computation it performs on behalf of the client.</p><p>Suppose:</p><ul><li><p>Alice possesses a valuable quantum state <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|\\phi\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, a proprietary quantum algorithm <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;U&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and only limited quantum computation resources (e.g., some quantum memory and the ability to execute simple Pauli gates).</p></li><li><p>Bob is willing to rent out access to his universal quantum computer.</p></li></ul><p>A BQC protocol allows Bob to act as Alice&#8217;s delegate. Bob computes <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;U|\\phi\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and returns the result to Alice, while learning nothing about either <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;U&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> or <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;|\\phi\\rangle&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p><p>The BFK protocol, proposed in 2008 (<em><a href="https://arxiv.org/abs/0807.4154">Universal blind quantum computation</a></em>, published in 2009), removed any need for quantum memory or quantum gates on the client&#8217;s side: the client only prepares random single qubits, yet can have arbitrary quantum algorithms executed blindly. In 2016, Takeuchi et al. (<em><a href="https://arxiv.org/abs/1607.01568">Fault-tolerant verifiable blind quantum computing with logical state remote preparation</a></em>) extended the BFK framework with stronger theoretical fault tolerance, which allows the server to execute longer gate sequences and tolerate higher levels of noise.</p><p>In 2025, Baranes et al. (<em><a href="https://arxiv.org/abs/2505.21621">Designing fault-tolerant blind quantum computation</a></em>) designed an architecture that scales to fault tolerance while keeping the client&#8217;s requirements minimal:</p><ul><li><p>The client only needs the ability to measure server-sent photonic qubits in arbitrary bases (directions). The client does not need to store quantum states or perform quantum gates.</p></li><li><p>The server needs a QPI: matter qubits are repeatedly coupled to photons, which are sent to the client for measurement.</p></li></ul><p>This approach substantially reduces the cost of deploying BQC and broadens its market potential.</p><h4>Super Long Baseline Interferometry for Astronomy</h4><p>Quantum interconnects can be applied to astronomy. The basic idea is to exploit the nonlocal nature of quantum entanglement to (1) improve angular resolution by extending the baselines of astronomical interferometers, and (2) increase sensitivity by avoiding the need to physically transmit astronomical photons.</p><p>We first briefly introduce a few famous astronomical interferometer systems.</p><ol><li><p>Event Horizon Telescope (EHT). Conceptual and experimental work began in the early 2000s. The project was formally launched in 2009 and reached operational maturity by 2017. The EHT uses a technique known as Very Long Baseline Interferometry (VLBI). Telescopes distributed across the globe are first synchronized using atomic clocks. These telescopes then observe the same distant astronomical source simultaneously and record phase information in electrical signals with extremely precise timing. These signals are then brought to a central correlator facility, where timing offsets are corrected and the signals are computationally combined to produce interference fringes, from which an image of the astronomical source can be reconstructed. The EHT produced the first direct image of a black hole. In April 2017, 8 radio observatories around the world observed the target simultaneously, collecting roughly 3.5 PB of data over about 40 hours. After nearly 2 years of data processing and analysis, the black hole image was released in April 2019. The EHT operates at a wavelength of about 1.3 mm (230 GHz), in the millimeter-wave radio band. Moving to still higher observing frequencies is difficult due to factors such as the stringent timing requirements exceeding the capability of atomic clocks, and atmospheric absorption by water vapor. The EHT achieves an angular resolution of about 20 microarcseconds in the radio band. This is equivalent to distinguishing a ping-pong ball on the surface of the Moon from Earth.</p></li></ol><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!bTEF!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!bTEF!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp 424w, https://substackcdn.com/image/fetch/$s_!bTEF!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp 848w, https://substackcdn.com/image/fetch/$s_!bTEF!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp 1272w, https://substackcdn.com/image/fetch/$s_!bTEF!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!bTEF!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp" width="462" height="462" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/fd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1200,&quot;width&quot;:1200,&quot;resizeWidth&quot;:462,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;A dark center ringed by glowing orange light&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="A dark center ringed by glowing orange light" title="A dark center ringed by glowing orange light" srcset="https://substackcdn.com/image/fetch/$s_!bTEF!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp 424w, https://substackcdn.com/image/fetch/$s_!bTEF!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp 848w, https://substackcdn.com/image/fetch/$s_!bTEF!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp 1272w, https://substackcdn.com/image/fetch/$s_!bTEF!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Ffd9284e3-893a-4eac-8920-7d3f4ed9485b_1200x1200.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">The image of a black hole at the center of the M87 galaxy, released in April 2019. Source: <a href="https://www.eso.org/public/images/eso1907a/">EHT Collaboration</a></figcaption></figure></div><ol start="2"><li><p>Navy Precision Optical Interferometer (NPOI). Completed in 1994, the NPOI is a Y-shaped array with three 250-meter arms. Its siderostats can be moved between piers along the arms to vary the baseline length for adjusting the angular resolution. Starlight collected at the stations is then transported in vacuum pipes. Adjustable optical delay lines are deployed along the pipes to compensate for differences in path lengths so that the extremely faint light collected by the stations arrives simultaneously at a central beam-combining facility to execute interference. NPOI&#8217;s maximum design baseline is about 437 meters, corresponding to a theoretical angular resolution of about 0.2&#8211;0.4 milliarcseconds. Unlike the EHT, which operates at millimeter wavelengths, the NPOI operates at 450&#8211;850 nm, covering the visible spectrum. For comparison, the Hubble Space Telescope has a visible-light angular resolution of about 50 milliarcseconds.</p></li><li><p>Center for High Angular Resolution Astronomy (CHARA). With first fringes in 1999 and its dedication in 2000, the CHARA array has a maximum baseline of 331 meters. It operates across visible and near-infrared wavelengths at about 500&#8211;2,500 nm, corresponding to angular resolutions of about 0.3&#8211;1.5 milliarcseconds, depending on wavelength. Like the NPOI, CHARA transports the faint starlight collected by its telescopes through vacuum pipes to a central beam-combining facility to execute interference. The array consists of 6 telescopes. Pairing the telescopes provides 15 distinct baselines.</p></li></ol><p>Both NPOI and CHARA share a fundamental limitation: to improve angular resolution requires longer baselines, but that means transporting faint starlight over longer distances, which increases loss and phase fluctuations. Measuring the light separately at each station instead, as radio VLBI does with local oscillators, introduces vacuum noise from zero-point fluctuations, which is too much for faint starlight.</p><p>Is there a way to interfere the starlight captured at spatially separated observatories without physically transporting the starlight?</p><p>Yes, there is: by performing nonlocal interferometry.</p><p>The basic idea was proposed around 2011 by Gottesman et al. (<em><a href="https://arxiv.org/abs/1107.2939">Longer-Baseline Telescopes Using Quantum Repeaters</a></em>). In the same year, Mankei Tsang (<em><a href="https://arxiv.org/abs/1108.1829">Quantum Nonlocality in Weak-Thermal-Light Interferometry</a></em>) showed that in the weak-light regime, nonlocal approaches that measure the light from both stations jointly achieve strictly higher precision than local approaches that measure each station separately and then combine the results, such as the heterodyne detection used in radio VLBI.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!IKKG!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!IKKG!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp 424w, https://substackcdn.com/image/fetch/$s_!IKKG!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp 848w, https://substackcdn.com/image/fetch/$s_!IKKG!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp 1272w, https://substackcdn.com/image/fetch/$s_!IKKG!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!IKKG!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp" width="433" height="531.2230623818525" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:649,&quot;width&quot;:529,&quot;resizeWidth&quot;:433,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Paper figure: receivers L and R of two telescopes share an entangled state from a central source and use it for an interference measurement&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Paper figure: receivers L and R of two telescopes share an entangled state from a central source and use it for an interference measurement" title="Paper figure: receivers L and R of two telescopes share an entangled state from a central source and use it for an interference measurement" srcset="https://substackcdn.com/image/fetch/$s_!IKKG!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp 424w, https://substackcdn.com/image/fetch/$s_!IKKG!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp 848w, https://substackcdn.com/image/fetch/$s_!IKKG!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp 1272w, https://substackcdn.com/image/fetch/$s_!IKKG!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0c12508e-82c7-44a2-b2a9-770a2b56145a_529x649.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">From Gottesman et al. 2011</figcaption></figure></div><p>In 2025, Stas et al. (<em><a href="https://arxiv.org/abs/2509.09464">Entanglement assisted non-local optical interferometry in a quantum network</a></em>) demonstrated nonlocal interferometry using weak laser pulses as stand-ins for starlight. The two stations were about 6 meters apart; spools of optical fiber extended the effective baseline to 1.55 km.</p><p>Their experimental procedure:</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!fUnn!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!fUnn!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp 424w, https://substackcdn.com/image/fetch/$s_!fUnn!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp 848w, https://substackcdn.com/image/fetch/$s_!fUnn!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp 1272w, https://substackcdn.com/image/fetch/$s_!fUnn!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!fUnn!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp" width="612" height="306.5964912280702" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:514,&quot;width&quot;:1026,&quot;resizeWidth&quot;:612,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Paper figure: two telescopes linked by quantum memories and optical fiber perform nonlocal interferometry: signal light collection, photon erasure, then nonlocal heralding and phase measurement&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Paper figure: two telescopes linked by quantum memories and optical fiber perform nonlocal interferometry: signal light collection, photon erasure, then nonlocal heralding and phase measurement" title="Paper figure: two telescopes linked by quantum memories and optical fiber perform nonlocal interferometry: signal light collection, photon erasure, then nonlocal heralding and phase measurement" srcset="https://substackcdn.com/image/fetch/$s_!fUnn!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp 424w, https://substackcdn.com/image/fetch/$s_!fUnn!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp 848w, https://substackcdn.com/image/fetch/$s_!fUnn!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp 1272w, https://substackcdn.com/image/fetch/$s_!fUnn!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2d4b2b18-24ee-4743-86d8-3caed71fb938_1026x514.webp 1456w" sizes="auto, 100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image buttonBase-GK1x3M"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon-noB79L"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image buttonBase-GK1x3M"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2 icon-noB79L"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">From <a href="https://arxiv.org/abs/2509.09464">Stas et al. 2025</a></figcaption></figure></div><ol><li><p>Each of the 2 stations is equipped with a quantum memory with 2 qubits: a memory qubit and a communication qubit. We denote the memory qubits by <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;m_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;m_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, and the communication qubits by <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>The 2 stations prepare an entangled pair in the antisymmetric Bell state <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;(|\\uparrow\\downarrow\\rangle - |\\downarrow\\uparrow\\rangle)/\\sqrt{2}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and store them in their memory qubits <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;(m_1,m_2)&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, which provide a longer coherence time.</p></li><li><p>An astronomical photon may arrive at any time in a spatial superposition over the 2 stations.</p></li><li><p>When an astronomical photon arrives, with some probability it interacts with the communication qubit at each station, which writes its information into <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>Interfere the astronomical photon on a beam splitter with a weak coherent pulse from a local oscillator, whose photon number is itself uncertain. This erases the possibility of telling which station the astronomical photon arrived at, which preserves its spatial superposition.</p></li><li><p>At each station, execute a CNOT gate over its qubits, with the memory qubit acting as the control. Recall that <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;(m_1,m_2)&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> were prepared in an entangled state. If <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> contain information from the astronomical photon, that information has been transferred into the joint state of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;(m_1,m_2)&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li><li><p>Measure <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> (specifically their spin direction). In an even outcome (both spin up or both spin down), we know for sure that the astronomical photon was successfully captured by the system. In an odd outcome, the photon was not captured.</p></li><li><p>Conditioned on successful photon capture, the system is now in a state <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;(|\\downarrow_L \\uparrow_R\\rangle - e^{\\pm i \\phi} |\\uparrow_L \\downarrow_R\\rangle)/\\sqrt{2}&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. The sign depends on the spin directions measured for <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_1&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;c_2&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>. We are interested in <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\phi&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>, the relative phase of the astronomical photon&#8217;s spatial superposition between the 2 stations.</p></li><li><p>Measure the above system state.</p></li><li><p>Repeat steps 2&#8211;9 many times to statistically estimate the value of <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\phi&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span>.</p></li></ol><p>Given <span class="latex-inline" data-attrs="{&quot;persistentExpression&quot;:&quot;\\phi&quot;,&quot;id&quot;:&quot;&quot;}" data-component-name="InlineLatexToDOM"></span> and system parameters such as the baseline length, we can infer the position of the astronomical source and reconstruct its image.</p><p>One can imagine a future network of nonlocal interferometric stations distributed across the globe. To achieve even longer baselines and avoid the atmospheric interference from water vapor, we could deploy the system on a network of satellites. Such systems would allow humanity to probe the mysteries of the starry sky in greater depth.</p>]]></content:encoded></item><item><title><![CDATA[GrayPunk]]></title><description><![CDATA[A Cypherpunk Guide for the Age of Lying Flat]]></description><link>https://newsletter.parity.fund/p/graypunk</link><guid isPermaLink="false">https://newsletter.parity.fund/p/graypunk</guid><dc:creator><![CDATA[mashbean]]></dc:creator><pubDate>Fri, 04 Sep 2026 10:52:00 GMT</pubDate><enclosure url="https://substack-post-media.s3.amazonaws.com/public/images/dbd95832-f114-4578-9d7f-4868001f34e6_1200x630.jpeg" length="0" type="image/jpeg"/><content:encoded><![CDATA[<p><em>Originally published at <a href="https://parity.fund/graypunk/?utm_source=substack&amp;utm_medium=email&amp;utm_campaign=graypunk">parity.fund/graypunk/</a> &#183; &#20013;&#25991;&#29256; &#8594; <a href="https://parity.fund/zh/graypunk/?utm_source=substack&amp;utm_medium=email&amp;utm_campaign=graypunk">parity.fund/zh/graypunk/</a></em></p><blockquote><p><em>&#8220;Turn the whole world ninety degrees and people will discover a truth that is usually hard to say out loud: lying flat is the true way of standing, and those who stand are the ones crawling.&#8221; &#8212; the Lying Flat Manifesto</em></p></blockquote><h2>Lying Flat Is Nothing to Be Ashamed Of, and It Works</h2><p>In recent years there have been two kinds of people around me: those who will remake themselves by any means necessary in order to close in on their ideals, and those who lie flat. People who lie flat, for whatever assortment of reasons, are seldom seen rousing themselves for any particular cause. They have lost the desire to act, above all the desire for political action, which in Hannah Arendt&#8217;s eyes is what most fully reveals what it is to be human, and so this group is not easy for those who act to reach. Meanwhile, the more capable of action a person is, the lonelier they tend to be. Much of the time they have already given up wasting their breath on people who lie flat, especially in the field of tool development, even though this runs against the very direction they set out in, which was to make the world better.</p><p>Oddly enough, though, both kinds of people are willing to keep company with me. Perhaps it is because I have knocked around inside governments and large organizations and can also live inside cooperatives and decentralized autonomous organizations. I can speak both languages. I have tried to wake friends who were lying flat with their eyes shut on purpose, and I have tried to persuade people who had gone too far out to slow down. Later I realized that this was, in Mencius&#8217;s phrase, climbing a tree to catch fish. Seen from another angle, lying flat may be the true way of standing; and if it is possible to close in on your ideals while lying down, that would bear out an old saying: one person can walk fast, but a hundred people can usually walk far.</p><p>Genuinely beneficial technology may owe its mass diffusion to the lazy many. As Kevin Kelly put it, echoing McLuhan, humans are the sex organs of technology. A technology without sex organs, without humans, cannot evolve, and however good a technology is, if it never gets the chance to reproduce it remains idle talk among the sex organs, which is to say among us. Groups, on the other hand, generate all sorts of synergies that no one could foresee at the outset: herd immunity in public health, collective security in international relations, emergent collective intelligence in complexity science.</p><p>I therefore hold that the technology best suited to lying flat is the technology best suited to reproducing. This essay dwells on the state of mind of lying flat while keeping your edge, and works out how it might push us toward the technological applications we actually need, above all in the cypherpunk domain, which of all fields most demands that you practice what you preach with your own body. In the cypherpunk world, the paragon in pursuit of perfection, the &#8220;complete person&#8221; that Confucian moral education holds up and almost no one becomes, must take up every sort of tool, habit and way of living in order to erase their own footprints and hide themselves properly. Being that kind of paragon is far too much work. Wage cattle (shachiku, as East Asian office workers have learned to call themselves: livestock kept by the company) really have no spare time for following paragons. Even in the most extreme political environments, with everyone jumping at shadows, the most that wage cattle can manage is Soviet-era kitchen talk: expressing themselves a little, after dinner, in the one space nobody is watching. And even when wage cattle get curious enough about the world of privacy and security to sign up for a talk, they forget everything the moment the talk ends.</p><p>The paragon, the forerunner and the prophet shine too brightly, and it is genuinely unclear whether that is a good thing or a bad one; long before the day of deliverance arrives, the prophet has already ascended. Better to be an ordinary person, a tree hidden in the forest. But today&#8217;s society rewards the people holding hammers, the entrepreneurs, developers, storytellers, influencers and public intellectuals, and the crowd loves watching them hammer nails everywhere, which is exactly what gives away their position. Like the Pied Piper, they pipe the rats everyone wants to beat out into the river, and the forest that hid the trees is stripped bare.</p><p>This produces a paradox in the cypherpunk world: the people hawking and evangelizing good privacy tools are the most conspicuous people in it. Even if they hold the finest invisibility cloak going, they have to take it off for a while. To carry out their &#8220;missionary&#8221; work and get more people wearing invisibility cloaks, they must temporarily switch off their own invisibility.</p><p>So this essay tries to work out how to be a lazy cypherpunk: how to find, somewhere between the paragon and the wage cattle, a state with room for both, and how, inside the &#8220;spiritual civilization&#8221; of collective lying flat (to borrow a phrase the Chinese state is fond of), to let the technologies that protect ourselves and our groups be built out slowly. Cypherpunk can still be cool, but perhaps the coolness can live in the lining rather than on the face, with a gray coat worn over the top. This we call GrayPunk.</p><p>Steady, low-key technological diffusion may be an important idea for anyone thinking about survival technology. What I care about, therefore, is how to make the general public secure enough, rather than how to forge an elite into paragons.</p><h2>When Self-Censorship Becomes a Knee-Jerk Reflex</h2><p>The previous section discussed those who lie flat and those who act. Both are natural responses of an individual under pressure from the collective, one response that splits into two entirely different directions. Set aside for the moment whether the reasons for that pressure are just, whether they accord with the spirit of the age, whether they violate human rights. Consider only the individual confronted by a force much larger than themselves, and borrow the language of the stress response: people produce the most basic biological reactions of fight, flight and freeze.</p><p>Those who act, fight. They stop at nothing, like a rose growing out of a crack in the concrete. Most of them fail, of course; the bird that sticks its head up gets hit. Those who lie flat neither fight nor have anywhere to run, and their condition is best compared to freezing, like a sheep playing dead, flopped in the road. Humans lie down too, inside the structures of society, lying flat through work, life and entertainment. Perhaps they have adapted; perhaps they have given up resisting. They have, in effect, stopped responding to the pressure at all. There is occasional discomfort, but on the whole they survive, and this state of mind is a common fixture in certain East Asian societies.</p><p>Let us go on to the culture of conformity in East Asian societies. By &#8220;East Asians&#8221; this essay means, specifically, people shaped by the Confucian cultural sphere. We are in the habit of not expressing ourselves in public; sometimes even raising a hand to speak feels like enormous pressure. &#8220;Being the same as everyone else&#8221; may be one of the great survival habits, and after years upon years of socialization, trying to be the same as everyone else has become a knee-jerk reflex. Reading the air, as the Japanese put it, not being a bother to other people, even managing your own body odor: these all belong to the same cluster of concepts, the etiquette of taking up as little space as possible.</p><p>A culture of conformity like this does not even need top-down oppression to produce a kind of endogenous self-censorship all by itself. Before we put forward an unorthodox opinion, we run once through the whole tangle: will this sound abrupt, will other people fail to understand it, will it become a burden to them? That is self-censorship in its most basic form. And the ruler we measure with comes from a collective consciousness we imagine for ourselves. Although we call it collective consciousness, it is in fact tucked away separately inside each of us, so it might be more precise to define it as &#8220;the collective consciousness each individual privately supposes to exist.&#8221;</p><p>But precisely when everyone holds such a collective imagining, collectivity emerges. Let that collectivity iterate through enough behavior, trial, error and correction, and a dynamic collective consciousness is thereupon born, which may well be the origin point of conforming behavior. This is not the happy outcome that Benedict Anderson&#8217;s &#8220;imagined communities&#8221; are supposed to bring. We can of course call it an aggregate of national or cultural character, but on the darker reading, when self-consciousness willingly gives itself over to the collective consciousness, conformity makes people feel safe, without actually guaranteeing it, and at the same time makes them banal.</p><p>Timur Kuran&#8217;s &#8220;preference falsification&#8221; and Elisabeth Noelle-Neumann&#8217;s &#8220;spiral of silence&#8221; complete the loop. People hide their private beliefs because they anticipate sanction or fear isolation; public space therefore overestimates support for the mainstream opinion, which reinforces the silence further. Jonathon Penney&#8217;s research on Wikipedia browsing likewise shows that after government surveillance was widely reported, views of certain sensitive articles fell: a chilling effect can reach even perfectly legal reading (Penney, 2016).</p><p>This means that anyone trying to make their way in society carries the neural circuitry of self-censorship built in at every moment. Think before you speak, think before you raise your hand, think before you act. And if that self-censorship appears in an authoritarian or even totalitarian political environment, where top-down oppression exists purely to maintain a hegemonic culture, then self-censorship and collective censorship really do become one thing. Over time, people who self-censor may even develop a tendency toward system justification, forming a strength-worshipping culture that takes pride in its own hegemon. Even when the individual is coerced by power, holding only duties and no rights without knowing it, this subtle state of mind still emerges.</p><p>How can we tell easily whether a culture of conformity contains oppression from above? Perhaps we can bring in the eyeball test proposed by the political philosopher Philip Pettit. When you face different people, a partner, a peer, a family member, a boss, a politician, a law-enforcement agency, do you avert your eyes and turn your head away? If you do, there is a good chance that the other party ranks above you in the abstract world of power, which may indicate that you are in a relationship of domination. Let us ask the question another way: if you look at yourself in the mirror while thinking about an issue difficult enough that you might have to censor it, will you avoid your own eyes?</p><p>So within the culture of conformity in East Asian societies, an atmosphere of surveillance is born in which collective censorship and self-censorship resonate and reinforce each other, and hundreds of millions of people live inside this panopticon. Inside the great ring is a small ring: the great ring is the watcher who seeps through every crack, the small ring is the self-restraint that, as the Buddhist saying goes, the mind gives birth to on its own. When censorship becomes ordinary, argot and irony arise to meet it, and the Sinophone world may well have built the most formidable civilization of argot anywhere on earth.</p><h2>Huddling Together for Warmth Against Collective Surveillance</h2><p>We often see puzzling posts on Chinese-language social platforms, posts that make you go around the loop twice before you understand what the author is trying to say. Or rather, who the author is trying to say it to, and who they are trying to keep it from. This is exactly the art of argot.</p><p>The first reason is that saying things straight carries a clear risk, which creates the demand for argot. Keyword filtering, for instance, is an extremely efficient digital literary inquisition. When a user&#8217;s post contains a keyword the powerful would rather not see, the post is taken down, the account is annihilated, or, more heart-stopping still, the user is &#8220;invited to tea,&#8221; the euphemism for a summons from state security. As top-down control and an internet culture of collective censorship gradually take shape, censorship dictionaries are slowly built up. Users, of course, gradually feel out the boundaries of the censorship tools, work out the forbidden phrases, and then naturally develop argot or irony so that plain keyword filtering cannot bite.</p><p>For the past decade or so, the common method of online text censorship was plain keyword filtering: if the keyword appeared in the post, the post came down. In the last few years, though, the arrival of large language models has brought a rapid leap in the ability to analyze context and intent, and combined with existing tools such as stylometry, the magic weapons for fishing out a particular user have leveled up enormously.</p><p>The second reason is that argot makes it easy to tell friend from foe. Whoever understands it belongs to your tribe; whoever does not is an outsider. Argot, or irony, has to accumulate through shared lived experience. It is not something a centralized standard dictionary, an authoritative university lecturer or a news editor can define. Every generation, every region, every community is likely to have its own, and in a public space where everyone is jumping at shadows, the point of having argot matters more still.</p><p>Words themselves are double: exactly the same sentence has entirely different readings in different contexts, and nothing has been encrypted at all. A simple piece of argot can strengthen someone&#8217;s trust in a stranger, because whoever can speak it shares at least one stretch of culture, a line from a cartoon, an anime, a film or a song, a political event of great weight, or a meme that simply emerged. All of these can be birthplaces of argot, and none of them can be planned in advance.</p><p>James C. Scott called the performance of deference in front of power the &#8220;public transcript,&#8221; and the critique preserved behind power&#8217;s back the &#8220;hidden transcript.&#8221; Argot is precisely the gray channel between the two: it lets the hidden transcript enter semi-public space while preserving room to deny and retreat (Scott, 1990). King, Pan and Roberts, studying Chinese internet censorship, found that censorship targets content with collective-action potential in particular; what argot preserves is therefore not only room for expression but the ability to recognize comrades and coordinate action (King, Pan &amp; Roberts, 2013).</p><p>Because double-meaning argot is not encrypted, anyone who puts in a little effort can pass as an insider quite easily; learn a few phrases and you can slip into the community. That is argot&#8217;s risk. But it is also why argot and irony develop so fast, fast enough that before the public has worked out whether someone supports or opposes a given position, whether they are being ironic or actually mean it, the evolving tribal code may already have shifted along another notch. At which point plenty of people inevitably think: &#8220;if it is this chaotic, I may as well give up trying to tell.&#8221; So more and more people lie flat, which can harden into rational ignorance and lead in turn to informational withdrawal and political disengagement.</p><p>But this is not comfortable lying flat; lying flat is not supposed to be this tiring. This particular inner journey toward lying flat is saturated with self-censorship. In a society full of digital literary inquisitions, citizens must consciously avoid certain places in order to escape disaster, and so their mental maps naturally sprout patch after patch of forbidden territory. This is lying flat saturated with self-censorship. To lie flat in genuine comfort, you have to untie the knots in your heart, smooth the mental map flat, and consciously undo the neural circuitry of the knee-jerk reflex.</p><p>There are two remedies here, one individual and one collective. On the individual side, you need to build digital hygiene habits without giving up on thinking. This does not require overdoing it: just put to work the atmosphere of constant conformity we already live in. Do not fall too far behind the group, and do not get too far ahead of it either, the old counsel of the mean. You will of course also need sound views on information security and privacy, and to judge, according to actual risk (your threat model), how far you really need to go. This is the way of living I call GrayPunk. The collective remedy is to make good-enough security practices the group default, so that not everyone has to keep up a high state of alert alone. The rest of this essay proceeds from there.</p><p>GrayPunk derives from cypherpunk, and the word cypherpunk borrows its name from cyberpunk. Cyberpunk works tend to imagine technological capability growing without limit while remaining pessimistic about civilization and its power relations. The future they depict is a human-machine composite in which class problems still exist and an extractive economy goes on plundering people and the environment; technology serves humans, but only the population at the top counts as human.</p><p>Cypherpunk took over cyberpunk&#8217;s name and tried to answer the dystopia it depicted with cryptography. Cypherpunk&#8217;s supporters lean anarchist; put bluntly, they do not much believe that governments, corporations or international organizations can guarantee an individual&#8217;s security. Security should begin with your own practice, including privacy tools and self-contained systems of exchange: currency, culture, language, network infrastructure and so on.</p><p>Cypherpunks are a very particular subcultural group, made up mainly of cryptographers, hackers with a will to political action, and academic circles. Few in number though they are, they have already become indispensable figures in the history of digital civilization, because they have won many battles in litigation against states and in the development of open-source technology, in the East as much as in the West. But there are plural value systems among cypherpunks too, the classic libertarian and the more left-wing spirit of solidarity, and plenty of each.</p><h2>GrayPunk as a New Punk</h2><p>But the GrayPunk this essay proposes does not require that kind of fervor, or that you be clever and hard-working, in order to join; it is a lay practice, not a monastic order. We might try peeling cypherpunk away from the Whig history that insists the world must eventually progress, and season it instead with the slacking spirit of lying flat. Perhaps a path of technological development like that is what actually moves civilization forward; who knows.</p><p>The Gray Man is a common term in operational security (OPSEC) and prepper communities. It means making yourself look ordinary in a crowd, unremarkable, not worth special attention, a common, low-cost strategy for hedging risk and countering surveillance. If a person is armed to the teeth, wearing a full set of high-end tactical gear and carrying specialized equipment, they may feel very safe, but in practice they have raised their own identifiability. The Gray Man&#8217;s reasoning runs the other way: blend into the environment, keep a low profile, make it hard for an observer to remember you and give them no reason to keep watching.</p><p>GrayPunk&#8217;s core spirit is not to develop an invisibility cloak beyond the world&#8217;s tech tree, but simply not to stand out from the crowd: to dim your light and mingle with the dust, as Laozi advised. This idea suits East Asian societies, which have spent whole lifetimes cultivating the spirit of conformity, extremely well, because to blend into a crowd you must be able to read a crowd, and the trick of self-censorship we have honed can be put to full use here, simply pointed in another direction. We know how to wear what everyone else is wearing, to go out and to raise a hand to ask a question at the right moment; we know how to get what we want without coming into conflict with anybody.</p><p>And still we know we are cool. That coolness is emphatically not external; no punk haircut, tattoos or nose ring required. The coolness is in the inner posture. We have our own punk spirit, tucked away beneath a gray coat, and this kind of coolness can find companions, and must have them. And because it is so much less difficult than cypherpunk, it can more easily reach a larger base, and more easily spread outward, slowly, from the niche, hard-to-implement layers of subculture.</p><p>What is more, a jump of an order of magnitude in numbers is itself the true practice of the cypherpunk spirit, because anonymity loves company. If real lying flat is to be achieved, then beyond individual security and daily habits, collective security is the second important subject. It is hard for one individual to compel others to cooperate in order to reach collective security; but if a whole society, or a whole tribe, adopts a set of not-so-difficult operating principles at the same time, path dependence will keep that set of principles alive inside the group for a very long time.</p><p>Even a society that runs on involution (neijuan, the East Asian word for competition that grinds everyone down without moving anyone forward), everyone trampling everyone else, still has a path toward safe lying flat. All it takes is for individuals to be consciously a little bit safer than the next person. We are all wearing gray, but when the predator comes hunting Gray Men, we have a few extra layers of protection and are more likely to slip through. People who think this way act, and over time the whole Gray Man community slowly upgrades its methods of protection, rather than balling up like a shoal of sardines and waiting for the sailfish to come and feed. We need to build second-order thinking into the development of technology and of digital literacy. Collective security is dynamic, and the best outcome is that the whole gradually levels up. That said, the long-run solution to this game cannot simply be to push risk onto more fragile people; it has to raise the overall security baseline step by step.</p><p>The history of the VPN illustrates exactly this kind of collective evolution, the kind the old proverb describes: the Way grows a foot taller and the demon grows ten. The VPN began as a rather boring piece of corporate information security: it let users outside the office connect safely into the company&#8217;s internal network through an encrypted tunnel. By the 2000s, open-source tools such as OpenVPN had gradually spread, and setting up your own encrypted tunnel had become easier and easier. At the same time, when China&#8217;s Great Firewall began carving up the network through DNS poisoning, IP blocking and keyword filtering, these tools, which had carried no revolutionary coloring at all, were quite naturally picked up to break through the block. The VPN at that point was very likely just something internet users reached for out of convenience, not a grand political act.</p><p>But the Great Firewall learns too. As more and more people used the same VPN tools, the traffic itself became an identifiable signature, so anti-censorship technology changed in turn. Shadowsocks, V2Ray and Tor&#8217;s various obfuscated transports were developed one after another, and the technical problem began shifting from plain encryption toward obfuscating traffic. Teams studying the Great Firewall found that since at least 2019, China&#8217;s censorship system has first used features such as packet length and entropy to guess whether a stream of traffic is Shadowsocks, then dispatched active probes to connect to the suspect server and confirm. By 2021 the Firewall had even begun identifying &#8220;fully encrypted&#8221; traffic at scale, affecting Shadowsocks, VMess and obfs4 alike. At this point, people using advanced technology look like soldiers in full battle rattle: once the outward appearance of your traffic departs from what a normal protocol looks like, it is very easily treated as an outlier.</p><p>So the development of obfuscation technology turned toward the Gray Man mode. The better the blockers get at hunting outliers, the more incentive anti-censorship tools have to imitate the normal, and the two sides co-evolve through round after round of identification, blocking, disguise and re-identification. The fight has already spread from protocols to regulations, app stores and commercial services, but the core is the same: the blocker looks for anomalies, and the user finds a way to melt back into normal traffic. Finn Brunton and Helen Nissenbaum call this kind of practice obfuscation, deliberately adding noise, ambiguity or plausible signals to make data harder to classify and exploit (Brunton &amp; Nissenbaum, 2015).</p><p>This is also where GrayPunk is genuinely easy to put into practice. The grand ideal of internet freedom does not end in a landscape where everyone has become a cryptographer; it may end with millions of people acquiring an utterly ordinary habit. When censorship levels up a little, the tools level up a little too; when the tools get too hard to use, somebody in the market finds a way to repackage them a little more simply. Every individual only needs to know a little more than they did yesterday. That is already pretty punk.</p><p>GrayPunk, then, is collective security, and collective security is hiding a tree in the forest. Across the long river of history we assume there is no natural predator of humans that will wipe out humanity in one go, only humans competing with each other, and so while there is no guarantee that every tree stays standing, the whole forest is hard to clear at a single stroke.</p><p>So when we discuss collective security we must take into account the art of non-resistance and the courage to coexist; after all, that is what life actually looks like. Conforming, self-censoring, living comfortably, being a little bit safer than the next person while also being a little bit cool: that spirit has lived in us for a long time already. In East Asian societies, cypherpunk is not necessarily a pure ideological ideal; it is a precondition for survival.</p><h2>Why Cypherpunk Never Went Mainstream, and How It Might Turn</h2><p>Look across the history of the internet and cypherpunk has plainly won a number of beautiful victories: private communication (E2EE), anonymous networking (Tor), digital signatures (PGP and its descendants), electronic money (Bitcoin, Ethereum, Monero, Zcash), ideas that have long since sunk deep into digital civilization. So why has cypherpunk remained stuck in a subcultural layer with few members and a very high barrier to entry?</p><p>More precisely, what struggles to go mainstream is cypherpunk as a self-aware political identity and way of life. The technologies cypherpunk created often do enter the mainstream, just wearing a different face. Once a tool truly spreads, people no longer need to understand its history, its ideology or its technical details; it takes off the punk leather jacket and becomes the default, by default. Users are protected by it every day without necessarily knowing where the protection came from. This may be exactly where cypherpunk is most successful and, at the same time, hardest to see.</p><p>What is cypherpunk, exactly? In &#8220;A Cypherpunk&#8217;s Manifesto,&#8221; published in 1993, Eric Hughes understood privacy as the power to selectively reveal oneself to the world. The individual cannot expect governments, corporations and other vast organizations to grant privacy out of goodwill, and so must build, together with others, systems capable of anonymous transactions and private communication. Cypherpunk&#8217;s best-known creed is the line &#8220;Cypherpunks write code&#8221;: a political position has to be realized as a technical tool, or it is just talk.</p><p>This gives cypherpunk the character of prefigurative politics. It does not merely make demands of existing institutions; it also tries to write a small part of the ideal order into the protocol in advance. Institutional design of this kind is in fact a rather left-wing imagining, because before the code, as before the law, everyone is equal. The approach replaces waiting for permission with building, and carries an egalitarian imagination; yet the formal equality the code provides can still be canceled out by inequalities of resources, capability and infrastructure, and so code, as an actor in a social movement, is caught in a dynamic loop. When petitions ask the powerful not to surveil the people, cypherpunk tries to make surveillance technically harder. When the law asks a government to respect freedom of speech, cypherpunk tries to build communication systems that no single government can easily shut down. When people ask a platform to treat its users well, cypherpunk tries to preserve the ability to export your data, start over elsewhere and leave the platform.</p><p>But the early cypherpunks sometimes also carried a strong technological inevitabilism. So long as cryptography kept developing and code kept spreading around the world, power, it seemed, would eventually be tamed by technology. That slides easily back into the Whig history criticized earlier in this essay, as though the tech tree had only one direction and every branch eventually led to freedom.</p><p>Reality is obviously messier. The same cryptography that protects dissidents also protects ransomware; the same distributed network that supports public collaboration can once again let a handful of nodes, exchanges and service providers monopolize it. Technology will not choose civilization&#8217;s direction for us on its own.</p><p>Technology clearly will not stop accelerating, then, but we can choose the direction of the acceleration. The decentralized accelerationism (d/acc) proposed by Vitalik Buterin can be read as an update to the cypherpunk spirit. The full sense of d/acc is &#8220;decentralized and democratic differential defensive acceleration,&#8221; where the d points at once to decentralization, democracy, differential and defensive. It acknowledges that technological development brings enormous benefits, and acknowledges too that technological stagnation can cause real harm, but accelerating technology should not be understood as flooring the pedal without a word of discussion. Different technologies shift the balance of power between attacker and defender, and so we must give priority to developing the technologies that make attack harder, recovery easier and power more distributed.</p><p>Defense here is not the same as waiting passively, nor the same as handing all power to a prophet who claims to be able to protect the public. What d/acc pursues is distributed defense: individuals, communities and local organizations each holding a degree of protective capability, so that when the system is attacked it does not collapse entirely because a single node has fallen, and ordinary people do not have to permanently surrender their data, their identity and their freedom of action in order to obtain security. A sovereign whose word cannot be trusted is, after all, the largest security hole of them all.</p><p>This kind of thinking pushes cypherpunk one step onward, from personal privacy to collective security and even to the defense of civilization. Encrypted communication protects a conversation between two people; information defense protects a whole society&#8217;s capacity for judgment. Multisig protects one person&#8217;s holdings; institutional checks, balances and resilience mechanisms protect an organization from single points of failure. What is being protected expands gradually from the hacker, the punk who, in Mencius&#8217;s phrase, looks after their own virtue alone, outward to communities, organizations, public health, the information environment and democratic institutions.</p><p>Seen this way, the truly important function of defensive technology is not necessarily to make the strongest people invulnerable. Its more important function is to reduce the fragility of ordinary people, so that after one upheaval and then another they still keep the chance to get up again. This connects precisely with what this essay calls lying flat while keeping your edge: the posture of security is not standing permanently on guard, but being able to lie flat with your mind at ease.</p><p>In 2026, the Ethereum Foundation, in its Mandate, organized the core principles it must uphold into CROPS: Censorship Resistance, Open Source, Privacy and Security. The Mandate places these principles above convenience in priority and treats them as non-negotiable. It goes on to propose that the way self-sovereignty is used must be able to resist extraction while also offering a seamless user experience.</p><p>&#8220;Seamless&#8221; matters especially. The cypherpunk community has long been prone to treating unusability as the price freedom must pay, but a self-sovereignty tool that only experts can operate safely offers no more than a formal choice. Ordinary people will end up handing their keys, data and judgment back to an intermediary anyway, because daily life has no room for a full-time ascetic practice of information security. Designers cannot ask users to endure a terrible interface forever in order to defend a principle. On the contrary, designers must work to make censorship resistance, open source, privacy and security ordinary enough that ordinary people can go on being protected without renewing their vows every day. Only then can ordinary people join the ranks of the Gray Men.</p><p>I once proposed the idea of a Defense Transformation Guide, an attempt to offer a set of everyday methods for moving toward self-sovereignty and collective solidarity. When we talk about digital transformation today, society seems to suffer from neophilia; it likes to reward the people who invent new things. People like new platforms, new protocols, new artificial intelligence, new governance models and new startups, and they like watching founders wander around with a hammer looking for nails. As for maintenance? That is an afterthought nobody cares about. But as d/acc puts it, the axis of technological development can in fact be steered collectively by a population, and so I have been looking, in the space between collective solidarity and individual self-sovereignty, for the cypherpunk-rooted technologies and the latent next-generation techniques that belong there.</p><p>In the course of gathering and classifying these technologies, I found that cypherpunk still is not mainstream. There are many reasons; let us take them one at a time.</p><h3>i. If It Isn&#8217;t Radical, It Isn&#8217;t Cool</h3><p>A subculture needs to be a minority, but security needs to be collective. A large part of what makes punk cool is its distance from mainstream society. Once everybody can do a thing, it struggles to go on serving as a badge of identity. This leaves cypherpunk with an internal contradiction: it wants more people using privacy tools, but as soon as the tools spread, the special identity that came with the tools loses its value.</p><p>Inside a subculture, difficult knowledge, rare tools, special language and a high cost of practice can all become a form of subcultural capital. In cypherpunk, someone who runs their own server, verifies software signatures, knows how to compile code and is fluent in anonymous network protocols is of course worth admiring. But when those same skills are also used to prove who is cooler, technical ability hardens into rank within the community.</p><p>Argot cuts both ways here too. In an oppressive environment, argot helps comrades recognize each other and dodge crude text censorship; once it enters a technical community, it can turn into a gatekeeping mechanism. A newcomer who does not know what a seed phrase, entropy, a key or obfuscation means will struggle to take part in the conversation. This is particularly dangerous for information security. Security requires people willing to admit they do not understand something, and willing to admit they have been scammed before. The identity boundary originally used to recognize comrades can also get in the way of genuine mutual aid.</p><p>Cypherpunk communities are also prone to disputes over orthodoxy, over who is the true ascetic. Using that operating system is not secure enough; keeping data on that cloud is not independent enough; not self-hosting a node is not decentralized enough; still using mainstream social platforms is not resistant enough. Each criticism looks reasonable on its own, but add them together and the only qualifying cypherpunks left are the handful of people who can pour in vast amounts of time, money and specialist knowledge.</p><p>When a tool requires the user to complete an identity conversion and accept an entire worldview before they qualify for basic protection, it will struggle to enter the daily life of wage cattle. This gives cypherpunk a perverse incentive: the community most readily rewards whoever is furthest out in front, and does not necessarily reward whoever makes existing technology more boring, more stable and easier to use. Inventing a new protocol is cool; writing the missing documentation for an old protocol is less cool. Proposing the most extreme threat model is cool; working out a good-enough configuration for ordinary people is less cool. Declaring every mainstream platform unusable is cool; designing a path that lets users migrate gradually is less cool. But technological diffusion usually depends on that second, less cool kind of work.</p><h3>ii. Security Fatigue</h3><p>The second reason cypherpunk cannot go mainstream is security fatigue. As the previous section said, ordinary people cannot become paragons. A perfect cypherpunk needs a password manager, hardware security keys, encrypted drives, anonymous networking, an independent email service, separate identities for separate purposes, end-to-end encrypted messaging, offline backups and self-hosted services. They have to update software regularly, audit permissions, verify downloaded files, rotate keys and rehearse their recovery procedure, and to watch at every moment for locations showing up in their photos, metadata left behind in their documents, and whether their browser has formed a unique fingerprint.</p><p>NIST describes security fatigue as the weariness and resistance people develop when facing computer security. When warnings, password rules and security decisions come too frequently, people easily feel powerless, and go on to ignore the warnings and adopt riskier behavior. The heart of this problem is not that users lack knowledge; many have simply been bombarded for years by security demands beyond their cognitive load.</p><p>The design emphasis of low-friction security, then, is not only on educating the user but on reducing the number of security decisions the user has to remember, judge and repeatedly carry out. Tactical Tech&#8217;s Holistic Security places digital, physical, organizational and psychosocial security inside a single framework. A security regime that exhausts the people practicing it cannot last.</p><h3>iii. You Can&#8217;t Lie Flat Without Money</h3><p>The third reason cypherpunk cannot become mainstream is that maintaining technology takes resources. Open source can be distributed for free, but continuous maintenance still has to be paid for, and a surprising number of open-source projects critical to the world are maintained by one or two volunteers. The world has now reached the era in which these volunteers of the networked world are withering away, one by one, for reasons of health. Once a maintainer burns out, falls ill or leaves, an entire ecosystem can be exposed to risk. Steven Jackson&#8217;s &#8220;broken world thinking&#8221; warns us that technological order continues mainly through repair, care and maintenance; this work is less conspicuous than inventing a new protocol, but it decides whether a system lives (Jackson, 2014).</p><p>Privacy tools also face a peculiar commercial predicament. A lot of free consumer technology profits by collecting user data, serving ads and predicting behavior, but a service that protects privacy would collide with its own mission if it adopted the same model. Signal has explained publicly that maintaining a global private-communication service requires enormous infrastructure and development spending, and that the surveillance business model has spent years leaving users with the mistaken impression that consumer technology ought naturally to be free. Commercialization is not inherently a betrayal. The real question is whether the source of revenue is aligned with the user&#8217;s security. Subscriptions, cooperatives, public procurement, foundation grants, paid technical support, cross-subsidy and public-goods funding could all be remedies.</p><p>And making security the default itself requires steady funding, maintenance and documentation work.</p><p>The security technologies that have genuinely gone mainstream in history have usually completed one act of de-ritualization.</p><p>The spread of HTTPS did not depend on every website administrator in the world becoming a cryptographer. Let&#8217;s Encrypt lowered the cost of deployment with a free, automated and open certificate service, and the ACME protocol made requesting and renewing certificates something that could be automated at scale. In 2020 Let&#8217;s Encrypt issued its billionth cumulative certificate, and it treated usability and automation directly as the essential foundations of that diffusion. End-to-end encrypted messaging entered ordinary life without billions of people first understanding key exchange. In 2016 WhatsApp made end-to-end encryption the default state for calls and messages; users did not have to switch encryption on, and did not even have to know encryption was happening.</p><p>Together these cases show that technology rarely enters the mainstream because everyone has accepted a complete political philosophy. It enters the mainstream because the cost fell, the operations vanished, and the setting became the default. Cypherpunk technology&#8217;s most successful moments are usually also the moments when it looks least like cypherpunk. Every day, our connections, conversations and devices are already protected by those ideas. The revolution is absorbed by the establishment, and that, perhaps, is what technology actually reproducing looks like.</p><h3>iv. The Ant Cannot Shake the Tree</h3><p>The fourth reason cypherpunk cannot become mainstream is the extreme asymmetry of power. One developer can invent a new anti-censorship protocol, but the state holds far more power at the same time. The VPN history recounted above has already shown that this is a co-evolution with no endgame. If what cypherpunk imagines is one beautiful technical counter-kill, reality will usually disappoint. States and large platforms can lose a round, but as the old saying goes, a hundred-legged centipede does not stiffen the moment it dies; they will not fall apart on their own any time soon.</p><p>But an ant does not necessarily have to push a tree over head-on, and a forest does not survive on any single tree. A forest&#8217;s resilience comes from the symbiotic relationships between different species. Part of what stands above ground may be felled while the root system below still holds the ability to grow back. The real goal of anti-censorship technology, therefore, is not necessarily to destroy the censor in one blow. It can be to keep raising the cost of total control, to preserve alternative channels, to slow the lock-in of power, and to make sure knowledge and relationships do not disappear along with any single tool.</p><p>A single tool is easy to target; an ecosystem can turn, change shape and regenerate. This is precisely why GrayPunk must emphasize collective security. No individual needs the capability to defeat a state, but the group as a whole needs to avoid betting all its hope on one prophet, one paragon.</p><p>These four reasons are in fact interlocked. Subcultural boundaries obstruct diffusion, excessive operating costs obstruct practice, a lack of resources obstructs maintenance, and asymmetry of power makes it hard for any single victory to become a permanent result. The remedy must therefore lower the cost of identity, the cost of operation, the cost of maintenance and the cost of confrontation all at once. Cypherpunk needs to shift gradually from a heroic narrative into daily life, from the extreme security of a few paragons to the proportionate security that most ordinary people can sustain over the long run.</p><h2>GrayPunk as a Fashion</h2><p>The most interesting thing about fashion is that people usually imitate first and understand afterward. Most people do not read a whole history of clothing, a course in textiles and a body of identity politics before deciding what to wear today. They watch the people around them, see that some practice looks convenient and good, and adopt it. Fashion is therefore a low-cost mechanism of group coordination. It does not require every participant to share a complete theory; it only requires that a practice have a low enough threshold for imitation.</p><p>This is exactly what lets us repurpose the conformity nerve of East Asian societies.</p><p>Conformity originally taught people to read the air, censor themselves and avoid standing out; GrayPunk tries to turn that same capability toward collective security. When the people around you all use a password manager, turn on a device passcode, update regularly, use encrypted messaging and cut back unnecessary permissions, the individual does not have to feel they are taking part in a revolution. They are only doing what everyone else is doing.</p><p>GrayPunk has no uniform. If a particular set of signs were required, that aesthetic would already have lost the gray coat&#8217;s function. GrayPunk can have a shared posture, but it should not fix that posture into something easily recognized. GrayPunk is fluid. It spreads more the way a habit spreads than the way a costume does. GrayPunk is therefore a subculture without a subcultural uniform. It keeps punk&#8217;s distrust of power, its insistence on autonomy and its imagination of alternative systems. Its coolness is hidden where you cannot see it at first glance.</p><p>Laziness, besides, is also a fashion. The laziness meant here is a long way from negligence. Negligence is knowing the risk and leaving the problem to your future self; lazy design demands that the system handle the repetitive, trivial and error-prone work in advance. GrayPunk therefore treats laziness as a formal engineering specification. Important choices should appear at the moments that genuinely carry meaning, and the rest of the work should be borne by tools, organizational norms and infrastructure. If security only holds when you are alert, have plenty of time and are running high on political passion, then it is not security fit for human society.</p><p>Cool is where you cannot see it at first glance.</p><p>GrayPunk&#8217;s coolness can be measured in a counterintuitive way. The less a security technology demands the user&#8217;s attention to itself, and the more it preserves the user&#8217;s autonomy at the same time, the closer it comes to GrayPunk. The best protection is usually like the fire piping inside a building: nobody photographs it or checks in beside it on an ordinary day, but when the fire comes it decides who gets out of the building alive.</p><p>GrayPunk nevertheless faces one supremely important ethical question: if you lower your identifiability, does that steer you back toward self-erasure? Would it dissolve a subcultural group&#8217;s agency to advocate at all? The question is especially sharp in East Asian societies. If all we are doing is repackaging silence, obedience and the loss of one&#8217;s edges as a gray-coat strategy, that is already proof that power has won. Self-censorship does not become liberation automatically just because it has put on a punk name.</p><p>The difference between the gray coat and self-erasure can be identified through three tests: choice, reversibility and reciprocity.</p><p>The first is choice. Who exactly decides that a person should keep a low profile? If the answer is a boss, a government, a family, community opinion or internalized fear, then it is closer to coerced self-censorship. If the individual can still decide to whom, when and how much to disclose, then low visibility becomes part of privacy. This returns us to Eric Hughes&#8217;s understanding of privacy: the core of privacy is keeping the choice of whether to reveal oneself.</p><p>The second is reversibility. The gray coat should be a coat you can put on and also take off. An individual keeping a low profile in a high-risk environment should still preserve their name, their memories, their views, their relationships and their capacity to act inside the spaces they trust. They can tell the truth in the kitchen, they can recognize and be recognized among comrades, they can leave testimony when the conditions are right, and they can walk back into public space when they must. A strategy of invisibility you can never exit is more wretched than the panopticon.</p><p>The third is reciprocity. Does the gray coat make the whole forest denser, or does it only get you behind somebody else? If an individual shifts risk onto people who are more conspicuous, poorer or less technically capable, that is still a competitive hedge. GrayPunk instead requires that an individual&#8217;s protection create a public spillover, making it easier for other people to get secure too. A real anonymity set cannot be built alone, and truly hiding a tree in the forest cannot mean hiding yourself while cutting down every tree around you.</p><p>This also echoes the eyeball test mentioned earlier. The gray coat does not ask people to keep their heads down forever; it asks them to preserve the ability to choose when to raise them. Real security is not making a person never dare to look power in the eye again; it is that when they decide to look, there is still a group behind them that will not vanish the instant they fall for a while. In Albert Hirschman&#8217;s language, the gray coat can be a limited exit: lowering exposure for now while preserving the capacity for voice later.</p><p>Nor does GrayPunk demand that everyone lying flat suddenly stand up. Those who lie flat can take part at low intensity. A person may be unwilling to become a public political activist, but they can live more safely; they can back up data, maintain documentation, fund infrastructure, and teach the people around them to use mature tools. This low-visibility maintenance work is itself part of collective security.</p><h2>In Closing: How to Be a Lazy Cypherpunk</h2><p>Having written this far: being a lazy cypherpunk does not actually require imagining yourself as the last member of the resistance, nor saving up for a bunker while you wait for the end of the world.</p><p>We should lie flat in order to win lying down.</p><p>Winning lying down, the gamer&#8217;s term for a victory your teammates carry you to, means stretching the confrontation into an endurance race. The opponent has to keep pouring resources into surveillance, identification, blocking and pursuit, while we fold security into ordinary life so that each evasion costs a little less and each recovery comes a little faster. When the controller&#8217;s cost of &#8220;stability maintenance,&#8221; to use the Chinese state&#8217;s own term, keeps rising, and the controlled need only preserve enough slack to avoid being fully controlled, lying flat can turn into an asymmetric advantage.</p><p>A warrior does not need full battle rattle to go and buy breakfast. Security should observe proportion too, and this can be called proportionate security. Strapping on every protective tool you can find will not necessarily make you safer, and may well give the game away, exposing your own peculiarity while producing psychological fatigue on top.</p><p>The lazy cypherpunk also needs a little security zen. Security zen means taking in new knowledge, practicing with tools that have already matured, and reviewing your own life regularly, without falling into panic over every piece of security news. Do not mistake anxiety for diligence, or complexity for security. A genuinely deep security practice often shows up as a handful of actions so ordinary they are disappointing.</p><p>This is also a game of being a little bit safer than the next person. In the short run, a bit more protection lowers your chance of being the easiest target to attack; over a longer horizon, the most stable strategy is still to raise the security baseline for more people together. Anonymity loves company: the fewer people using a given privacy tool, the more the act of using it becomes a fingerprint in itself, and only when there are enough users does it blend into the ordinary background. We can borrow the metaphor of k-anonymity here: when a person shares their visible features with enough other people, they are harder to single out. A single Gray Man cannot make a GrayPunk community.</p><p>So what we have to do is not to forge ourselves into tireless paragons. The GrayPunk sidesteps heroic martyrdom and also refuses numb surrender. They choose a way of living that can be kept up through being busy, being tired, being dumped, being laid off, being ill and living through a political winter. A genuinely reliable security habit has to still work on the days when a person has the least strength; a genuinely reliable collective has to keep running after one or two people have fallen.</p><p>The social-movement scholar Verta Taylor calls the state in which a movement preserves its organization, its relational networks and its collective identity through an ebb tide &#8220;abeyance,&#8221; which might be rendered as holding in latency (Taylor, 1989). Lying flat while keeping your edge can be read as this concept&#8217;s version for digital survival, or, going one step further, as a description of the state of mind of an indestructible, indolent activist.</p><p>Lying flat while keeping your edge is king, because only a sustainable life makes for a long resistance. Lie down comfortably, keep the system running, and stay in the same forest as your companions: that is the most sustainable posture available to a lazy cypherpunk.</p><div class="captioned-image-container"><figure><div class="image-link image2" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!AS3H!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg 424w, https://substackcdn.com/image/fetch/$s_!AS3H!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg 848w, https://substackcdn.com/image/fetch/$s_!AS3H!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg 1272w, https://substackcdn.com/image/fetch/$s_!AS3H!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg 1456w" sizes="auto, 100vw"><img src="https://substackcdn.com/image/fetch/$s_!AS3H!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg" width="1456" height="80" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/e003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:80,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:5932,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:&quot;image/svg+xml&quot;,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:&quot;https://newsletter.parity.fund/i/214878416?img=https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg&quot;,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!AS3H!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg 424w, https://substackcdn.com/image/fetch/$s_!AS3H!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg 848w, https://substackcdn.com/image/fetch/$s_!AS3H!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg 1272w, https://substackcdn.com/image/fetch/$s_!AS3H!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe003538c-c064-4384-88ab-0ed16cf74955_1456x80.svg 1456w" sizes="auto, 100vw" loading="lazy"></picture><div></div></div></div></figure></div><p><span>GrayPunk is the first essay of </span><a href="https://parity.fund/telescope-editions/?utm_source=substack&amp;utm_medium=email&amp;utm_campaign=graypunk">Telescope Editions</a><span>, Parity's essay grant. Text &#169; 2026 </span><a href="https://x.com/mashbean">Yen-Lin (mashbean) Huang</a><span>, published under </span><a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a><span>.</span></p>]]></content:encoded></item></channel></rss>