{"id":2464,"date":"2015-09-15T13:46:35","date_gmt":"2015-09-15T17:46:35","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=2464"},"modified":"2016-12-10T04:41:16","modified_gmt":"2016-12-10T09:41:16","slug":"bell-inequality-violation-finally-done-right","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=2464","title":{"rendered":"Bell inequality violation finally done right"},"content":{"rendered":"

A few weeks ago, Hensen et al., of the Delft University of Technology and Barcelona, Spain,\u00a0put out a paper<\/a>\u00a0reporting the first experiment that violates the Bell inequality in a way that closes off the two main loopholes simultaneously: the locality and detection loopholes. \u00a0Well, at least\u00a0with\u00a0~96% confidence. \u00a0This is big news, not only\u00a0because of the result itself,\u00a0but because of the advances in experimental technique needed to achieve it. \u00a0Last Friday, two renowned\u00a0experimentalists—Chris Monroe of U. of Maryland and Jungsang Kim of Duke—visited MIT, and in addition to talking about their own exciting ion-trap work, they did a huge amount to help me understand the new Bell test experiment. \u00a0So OK, let me try to explain this.<\/p>\n

While some people like to make it more complicated, the Bell inequality<\/a> is the following statement. Alice and Bob are cooperating with each other to win a certain game (the “CHSH game<\/a>“) with the highest possible\u00a0probability. They can agree on a strategy and share information and particles in advance, but then they can’t communicate once the game starts. Alice gets a uniform random bit x<\/em>, and Bob gets a uniform random bit y<\/em> (independent of x<\/em>). \u00a0Their goal is to output bits, a<\/em> and b<\/em> respectively, such that a<\/em> XOR b<\/em> = x<\/em> AND y<\/em>: in other words, such that a<\/i> and b<\/i> are different if and only if x<\/em> and y<\/em> are both 1. \u00a0The Bell inequality says that, in any universe that satisfies the property of\u00a0local realism<\/a><\/em>,\u00a0no matter which strategy they use,\u00a0Alice and Bob can win the game at most 75% of the time (for example, by always outputting a<\/em>=b<\/em>=0).<\/p>\n

What does local realism mean? \u00a0It means that, after she receives her input x<\/em>, any experiment\u00a0Alice can perform\u00a0in her lab has a definite result\u00a0that might\u00a0depend on\u00a0x<\/em>, on the state\u00a0of her lab, and on whatever information she pre-shared with Bob, but at any rate, not on Bob’s<\/em> input y<\/em>. \u00a0If you like: a<\/em>=a<\/em>(x<\/em>,w<\/em>) is a function of x<\/em> and of the information w available before the game started, but is not<\/em>\u00a0a function of y<\/em>. \u00a0Likewise, b<\/em>=b<\/em>(y<\/em>,w<\/em>) is a function of y<\/em> and w<\/em>, but not of x<\/em>. \u00a0Perhaps the best way to explain local realism is that\u00a0it’s the thing you believe in, if you believe\u00a0all the physicists babbling about “quantum entanglement” just\u00a0missed something completely obvious. \u00a0Clearly, at the moment two “entangled” particles are created, but before they separate, one of them flips a tiny coin and then says to the other, “listen, if anyone asks, I’ll be spinning up and you’ll be spinning down.” \u00a0Then the na\u00efve, doofus\u00a0physicists measure one particle, find it spinning down, and wonder how the other particle instantly “knows” to be spinning up—oooh, spooky! mysterious! \u00a0Anyway, if that’s how you think it has to work, then you believe in local realism, and you must predict that Alice and Bob can win the CHSH game with probability at most 3\/4.<\/p>\n

What Bell observed\u00a0in 1964 is that, even though quantum mechanics doesn’t let Alice send a signal<\/em> to Bob (or vice versa) faster than the speed of light, it still makes a prediction about\u00a0the CHSH game that conflicts with local realism. \u00a0(And thus, quantum mechanics exhibits what one might not have realized beforehand was even a logical possibility: it doesn’t allow communication faster than light, but simulating the predictions of quantum mechanics in a classical universe\u00a0would<\/em> require faster-than-light communication.) \u00a0In particular, if Alice and Bob share entangled qubits, say $$\\frac{\\left| 00 \\right\\rangle + \\left| 11 \\right\\rangle}{\\sqrt{2}},$$ then there’s a simple protocol that lets them violate the Bell\u00a0inequality, winning the CHSH game ~85% of the time (with probability (1+1\/\u221a2)\/2 > 3\/4). \u00a0Starting in the 1970s, people did experiments that vindicated the prediction of quantum mechanics, and falsified local realism—or so the story goes.<\/p>\n

The violation of the Bell inequality has a schizophrenic status in physics. \u00a0To many of the physicists I know, Nature’s violating the Bell inequality is so trivial and obvious\u00a0that it’s barely even worth doing the experiment: if people had just understood and believed<\/em> Bohr and Heisenberg back in 1925, there would’ve been no need for this whole tiresome discussion. \u00a0To others, however, the Bell inequality violation remains so unacceptable that some\u00a0way must be found around\u00a0it—from casting doubt on the experiments that have been done, to overthrowing basic presuppositions of science\u00a0(e.g., our own “freedom” to generate\u00a0random bits x<\/em> and y<\/em> to send to Alice and Bob respectively).<\/p>\n

For several decades, there was a relatively conservative way out for local realist diehards, and that was to point to “loopholes”<\/a>: imperfections in the existing experiments which\u00a0meant that local realism was still theoretically compatible with the results, at least if one was willing to assume a sufficiently strange conspiracy.<\/p>\n

Fine, you interject, but surely\u00a0no one literally<\/em>\u00a0believed these little experimental imperfections would be the thing that would rescue local realism?\u00a0 Not so fast. \u00a0Right here, on this blog, I’ve had people point to the loopholes as a reason to accept\u00a0local realism and reject the reality of quantum entanglement. \u00a0See, for example, the numerous comments by\u00a0Teresa Mendes in my\u00a0Whether Or Not God Plays Dice, I Do<\/a>\u00a0post. \u00a0Arguing with Mendes back in 2012, I predicted\u00a0that the two main loopholes would both be closed in a single experiment—and not merely eventually, but in, like, a decade. \u00a0I was wrong: achieving this milestone\u00a0took only a few years.<\/p>\n

Before going further, let’s understand what the two main loopholes are (or rather, were).<\/p>\n

The locality loophole<\/em> arises because the measuring process takes time and Alice and Bob are not infinitely far apart. \u00a0Thus, suppose that, the instant Alice starts<\/em> measuring her particle, a secret signal starts flying toward Bob’s particle at the speed of light, revealing her choice of measurement setting (i.e., the value of x<\/em>). \u00a0Likewise, the instant Bob starts measuring his particle, his doing so sends a secret signal flying toward Alice’s particle, revealing the value of y<\/em>. \u00a0By the time the measurements are finished, a few microseconds later, there’s been plenty of time for the two particles to coordinate their responses to the measurements, despite being “classical under the hood.”<\/p>\n

Meanwhile, the detection loophole<\/em> arises because in practice, measurements of entangled particles—especially of photons—don’t always succeed in finding<\/em> the particles, let alone ascertaining their properties. \u00a0So one needs to select those runs of the experiment where Alice and Bob both find\u00a0the particles, and discard all the “bad” runs where they don’t. \u00a0This by itself wouldn’t be a problem, if not for the fact that the very same measurement that reveals\u00a0whether the particles are there, is also the one that “counts” (i.e., where Alice and Bob feed x<\/em> and y<\/em> and get out a<\/em> and b<\/em>)!<\/p>\n

To someone with a conspiratorial mind, this opens up the possibility that the measurement’s success or failure\u00a0is somehow\u00a0correlated<\/em> with its result, in a way that could violate the Bell inequality despite there being no real entanglement. \u00a0To illustrate, suppose that at the instant they’re created, one entangled particle says to the other: “listen, if Alice measures me in the x<\/em>=0 basis, I’ll give the a<\/em>=1 result. \u00a0If Bob measures you in the y<\/em>=1 basis, you give the b<\/em>=1 result. \u00a0In any other case, we’ll just evade detection and count this run as a loss.” \u00a0In such a case, Alice and Bob will win the game with certainty, whenever it\u00a0gets played at all—but that’s only because of the particles’ freedom to choose which rounds will count. \u00a0Indeed, by randomly varying their “acceptable” x<\/em> and y<\/em> values from one round to the next, the particles can even make it look like x<\/em> and y<\/em> have no effect on the probability of a round’s succeeding.<\/p>\n

Until a month ago, the state-of-the-art was that there were experiments that closed the locality loophole, and other experiments that closed the detection loophole, but there was no single experiment that closed both of them.<\/p>\n

To close the locality loophole, “all you need” is a fast enough measurement on photons that are far enough apart. \u00a0That way, even if the vast Einsteinian conspiracy is trying to send signals between Alice’s and Bob’s particles at the speed of light, to coordinate the answers classically, the whole experiment will be done before the signals can possibly have reached their destinations. \u00a0Admittedly, as Nicolas Gisin once pointed out to me, there’s a philosophical difficulty in defining\u00a0what we mean by the experiment being “done.” \u00a0To some purists, a Bell\u00a0experiment might only be “done” once the results (i.e., the values of a<\/em> and b<\/em>) are registered in human experimenters’ brains! \u00a0And given the slowness of human reaction times, this might imply\u00a0that a real<\/em> Bell experiment ought to\u00a0be carried out\u00a0with astronauts on faraway space stations, or with Alice\u00a0on the moon\u00a0and Bob on earth\u00a0(which, OK, would be cool). \u00a0If we’re being reasonable, however, we can grant that the experiment is “done” once a<\/em> and b<\/em> are safely recorded in classical, macroscopic computer memories—in which case, given the speed of modern computer memories, separating Alice and Bob by half a kilometer can be enough. \u00a0And indeed, experiments starting in 1998 (see for example here<\/a>) have done exactly that; the current record, unless I’m mistaken,\u00a0is 18 kilometers<\/a><\/del>. \u00a0(Update:<\/strong><\/span> I was<\/em> mistaken; it’s 144 kilometers<\/a>.) \u00a0Alas, since these experiments used hard-to-measure photons, they were still open to the detection loophole.<\/p>\n

To close the detection loophole, the simplest approach is to use entangled qubits\u00a0that (unlike photons) are slow and heavy and can be measured with success probability approaching 1. \u00a0That’s exactly what various groups did starting in 2001 (see for example here<\/a>), with\u00a0trapped ions,\u00a0superconducting qubits, and other systems. \u00a0Alas, given current technology, these sorts of qubits\u00a0are\u00a0virtually\u00a0impossible to move miles apart from each other without decohering them. \u00a0So the experiments used qubits that were close together, leaving the locality loophole wide open.<\/p>\n

So the problem boils down to: how do you create long-lasting, reliably-measurable entanglement between particles that are very far apart (e.g., in separate labs)? \u00a0There are three basic ideas in Hensen et al.’s solution to this problem.<\/p>\n

The first idea is to use a hybrid system. \u00a0Ultimately, Hensen et al. create entanglement between electron spins in nitrogen vacancy centers in diamond (one of the hottest—or coolest?—experimental quantum information platforms today), in two labs that are about a mile away\u00a0from each other. \u00a0To get these faraway electron spins to talk to each other, they make them communicate via photons. \u00a0If you stimulate an electron, it’ll sometimes emit a photon with which it’s entangled. \u00a0Very occasionally, the two electrons you care about will even emit photons\u00a0at the same time. \u00a0In those cases, by routing those photons into optical fibers and then measuring the photons, it’s possible to entangle the electrons.<\/p>\n

Wait, what? \u00a0How does measuring the photons entangle\u00a0the electrons<\/em> from whence they came? \u00a0This brings us to the second idea, entanglement swapping<\/i>. \u00a0The latter is a famous procedure to create entanglement between two particles A and B that have never interacted, by “merely” entangling A with another particle A’, entangling B with another particle B’, and then performing\u00a0an entangled measurement on A’ and B’ and conditioning on its result. \u00a0To illustrate, consider the state<\/p>\n

$$ \\frac{\\left| 00 \\right\\rangle + \\left| 11 \\right\\rangle}{\\sqrt{2}} \\otimes \\frac{\\left| 00 \\right\\rangle + \\left| 11 \\right\\rangle}{\\sqrt{2}}\u00a0$$<\/p>\n

and now imagine that we project the first and third qubits onto the state $$\\frac{\\left| 00 \\right\\rangle + \\left| 11 \\right\\rangle}{\\sqrt{2}}.$$<\/p>\n

If the measurement succeeds, you can check that we’ll be left with the state $$\\frac{\\left| 00 \\right\\rangle + \\left| 11 \\right\\rangle}{\\sqrt{2}}$$ in the second and fourth qubits, even though those qubits were not entangled before.<\/p>\n

So to recap: these two electron spins, in labs a mile away from each other, both have some probability of producing a photon. \u00a0The photons, if produced, are routed to a third site, where if<\/em> they’re both there, then an entangled measurement on both of them (and a conditioning on the results of that measurement) has some nonzero probability of causing the original electron spins to become entangled.<\/p>\n

But there’s a problem: if you’ve been paying attention, all we’ve done is cause the electron spins to become entangled with some tiny, nonzero probability (something like 6.4\u00d710-9<\/sup> in the actual experiment). \u00a0So then, why is this any improvement over the previous\u00a0experiments, which just directly measured\u00a0faraway entangled photons, and also had some small but nonzero probability of detecting them?<\/p>\n

This leads to the third idea. \u00a0The new setup is an improvement because, whenever the photon measurement\u00a0succeeds, we know that the electron spins are there and that they’re entangled, without having to measure\u00a0the electron spins to tell us that<\/em>. \u00a0In other words, we’ve decoupled the measurement that tells us whether we succeeded in creating an entangled pair, from the measurement\u00a0that uses<\/em> the entangled pair to violate the Bell inequality. \u00a0And because of that decoupling, we can now just condition on the runs of the experiment where the entangled pair was there, without worrying that that will open up the detection loophole, biasing the results via some bizarre\u00a0correlated conspiracy. \u00a0It’s as if the whole experiment were simply switched off, except for those rare lucky occasions\u00a0when an entangled spin\u00a0pair gets created (with its creation heralded by the photons). \u00a0On those rare occasions, Alice and Bob swing into action, measuring their respective spins within the brief window of time—about 4 microseconds—allowed by the locality loophole, seeking an additional morsel of evidence that entanglement is real. \u00a0(Well, actually, Alice and Bob\u00a0swing into action regardless; they only find out later whether this was one of the runs that “counted.”)<\/p>\n

So, those are the main ideas (as well as I understand them); then there’s lots of engineering. \u00a0In their setup, Hensen et al. were able to create just a few heralded entangled pairs per hour. \u00a0This allowed\u00a0them to produce 245 CHSH games\u00a0for Alice and Bob to play, and to reject the hypothesis of local realism at ~96% confidence. \u00a0Jungsang Kim explained to me that existing technologies could have produced many more events per hour, and\u00a0hence, in a similar amount of time, “particle physics” (5\u03c3 or more) rather than “psychology”\u00a0(2\u03c3) levels of confidence that local realism is false. \u00a0But in this type of experiment, everything is a tradeoff. \u00a0Building not one but two labs for manipulating NV centers in diamond is extremely onerous, and Hensen et al. did what they had\u00a0to do to get a significant result.<\/p>\n

The basic idea here, of using photons to entangle longer-lasting qubits, is useful for more than pulverizing local realism. \u00a0In particular, the idea is a major\u00a0part of current proposals for how to build a scalable ion-trap quantum computer. \u00a0Because of cross-talk, you can’t feasibly put more than 10 or so ions in the same trap while keeping all of them coherent and controllable. \u00a0So the current ideas for scaling up involve having lots of separate traps—but in that case, one will sometimes need to perform a Controlled-NOT, or some other 2-qubit gate, between a qubit in one trap and a qubit in another. \u00a0This can be achieved using the Gottesman-Chuang technique of gate teleportation<\/a>, provided<\/em>\u00a0you have reliable entanglement between the traps. \u00a0But how do you create such entanglement? \u00a0Aha: the current idea is to entangle the ions by using photons as intermediaries, very similar in spirit to what Hensen et al. do.<\/p>\n

At a more fundamental level, will this experiment finally convince everyone\u00a0that local realism is dead, and that quantum mechanics might\u00a0indeed be the operating system of reality? \u00a0Alas, I predict that those who confidently predicted that a loophole-free Bell test could never be done, will simply find\u00a0some new way to wiggle out, without admitting the slightest problem for their previous view. \u00a0This prediction, you might say, is based on\u00a0a different kind of realism.<\/p>\n","protected":false},"excerpt":{"rendered":"

A few weeks ago, Hensen et al., of the Delft University of Technology and Barcelona, Spain,\u00a0put out a paper\u00a0reporting the first experiment that violates the Bell inequality in a way that closes off the two main loopholes simultaneously: the locality and detection loopholes. \u00a0Well, at least\u00a0with\u00a0~96% confidence. \u00a0This is big news, not only\u00a0because of the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[33,4],"tags":[],"class_list":["post-2464","post","type-post","status-publish","format-standard","hentry","category-bells-theorem-but-a-flesh-wound","category-quantum"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/2464","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2464"}],"version-history":[{"count":18,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/2464\/revisions"}],"predecessor-version":[{"id":2486,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/2464\/revisions\/2486"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2464"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2464"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2464"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}