6 ms·

Breaking Bell's Inequality with Monte Carlo Simulations in Python

122 points by Maro 2y ago

anxcna 2y ago
[flagged]
- kzrdude 2y ago
  Why not use numpy's rng?
- fancyfredbot 2y ago
  In which way is python's random module broken, specifically?
- jgalt212 2y ago
  I would assume the secrets standard library creation might be related to this concern. https://docs.python.org/3/library/secrets.html https://docs.python.org/3/library/secrets.html
danwills 2y ago
"a talented college physics student can do it" I'm afraid I don't qualify for being able to do that, but I feel like I'm tantalizingly close to understanding this overall - but I'm finding it hard to understand why the lower-right "TT" quadrant is transposed in the S=2.828 example (the red box in the diagram). Maybe it's obvious if one understands it better?
- n4r9 2y ago
  It requires a chunk of linear algebra to understand, but the Wikipedia page has a slightly more detailed explanation: https://en.wikipedia.org/wiki/Bell%27s_theorem#Theorem https://en.wikipedia.org/wiki/Bell%27s_theorem#Theorem It's related to the fact that the expected value of A_1 tensor B_1 is negative 1/sqrt(2), whilst the expected value of all other tensor products are positive 1/sqrt(2).
  - jahnu 2y ago
    The explanation and table in the Simple English page for this helped me grasp it better. (Although the diagram using green dots only confuses :) ) Greene's book is a fantastic read too! https://simple.wikipedia.org/wiki/Bell%27s_theorem https://simple.wikipedia.org/wiki/Bell%27s_theorem
    - gus_massa 2y ago
      > Although the diagram using green dots only confuses :) It's very confusing. In particular it does not say that the box have 3 doors until the middle of the explanations. Also, I don't find the example very similar to the Bell's Inequality. Moreover, I expect in a quantum system that when both open the same door they get the same result (or the oposite) so in a quantum system I expect that when both open the same door they get 100% (or 0%) agreement, so insted of 50% I expect 1/3 * 100% + 2/3 * 50 % = 66% (or 1/3 * 0% + 2/3 * 50 % = 33%). Anyway, in some versions of the Bell's Inequality the doors of the boxes are "misalignment" so on box has white-gray-black doors and the other has another ser of colors. let's say creme-pink-brown doors. You never have a 100% or 0% of coincidences of the results.
    - n4r9 2y ago
      This looks like some kind of variant of Bell's Theorem. I've not seen it before, but it reminds me of the GHZ inequality [0] [[EDIT - actually I take that back. The GHZ inequality refers to three systems whereas your link refers to three measurement choices]]. I don't think your link gives a derivation of the quantum correlations beyond "Quantum physics says that half the time they should get a match". [0] https://en.wikipedia.org/wiki/Bell%27s_theorem#GHZ%E2%80%93Mermin_(1990) https://en.wikipedia.org/wiki/Bell%27s_theorem#GHZ%E2%80%93M...
- Maro 2y ago
  Hi, I'm the guy who wrote the article. In the article, I first show how to "break" the Bell inequality without making a reference to any complicated math or Physics, this is the section "Breaking the Bell inequality with non-local information", which uses the dice roll example. This is on purpose, for pedagogical reasons, and this is why the Python approach imo is so useful to demonstrate this whole thing: the key idea is, to break the inequality, you need to "peek" at the other side. Then, the next mental step is simply the statement that, in "real life", you can prepare a composite system (eg. 2 photons modeled as 2 qubits) that you can seperate (modeled as the split() function in Python), you can send the 2 parts to two different observers, they use a certain measurement setup, and the whole game is played, statistic computed, etc. and then you get this value 2.82 (which breaks the Bell inequality)! So somehow, the 2 qubits are doing that we can only model [in Python] as peeking! The actual derivation of how to get that 2.82 is, in some sense, almost like a a detail. I think with this approach, even a non-physicist can understand what this whole argument is (=Bell's genius). "a talented college physics student can do it" - I'm a Physicist, but I'm not working as a Physicist, and I was able to derive all the numbers in that table by hand with pen & paper directly. I figured if I can do it 15 years out of school, so can a talented college physics student! The next article will be that derivation [of the raw probabilities], I just need to transcribe it from my notebook to Latex and clean it up. If you want to see the original notes: https://photos.app.goo.gl/sqxLnEhyeZTDD7oA6 https://photos.app.goo.gl/sqxLnEhyeZTDD7oA6
n4r9 2y ago
This is closely related to my PhD. It was many years ago but if I remember rightly there is no need for the assumption of determinism - Bell Inequalities hold just as well for random local hidden variables. Simulating the correlations with computer programs is an interesting idea, partly because it challenges to those who still believe in a "local" reality to demonstrate Bell Inequality violations in distributed classical computer systems. Back in the day there was a crackpot researcher named Joy Christian who kept publishing repetitive papers in the belief that geometric algebras provided a counterexample (it looks like he's still going strong! [0]). Of course, there's nothing about geometric algebras that cannot be modelled in a computer program, so in principle Christian should have been able to demonstrate Bell violations in a distributed scenario. Needless to say, this hasn't happened even though it would be a momentous breakthrough in the foundations of physics. [0] https://ieeexplore.ieee.org/document/9693502 https://ieeexplore.ieee.org/document/9693502
- eigenket 2y ago
  You know something has gone horrifically badly when a paper begins with > This reply paper should be read as a continuation of my previous reply paper [1], which is a reply published in this journal to a previous critique of one of my papers We're way too deep in replies now, and anyone who values their time should get out now.
  - 0cf8612b2e1e 2y ago
    On the other hand, academics slap fights are magnificently petty to behold. In any dispute the intensity of feeling is inversely proportional to the value of the issues at stake. That is why academic politics are so bitter.
    - n4r9 2y ago
      The conclusion reads like someone who can't admit they're wrong on Reddit: > The common defect in the critiques [2], [6], and [14] is that, instead of engaging with the original quaternionic 3-sphere model presented in my papers [1], [7]– [11] using Geometric Algebra, they insist on criticizing entirely unrelated flat space models based on matrices and vector “algebra.” This logical fallacy by itself renders the critiques invalid. Nevertheless, in this paper I have addressed every claim made in the critique [6] and the critiques it relies on, and demonstrated, point by point, that none of the claims made in the critiques are correct. I have demonstrated that the claims made in the critique [6] are neither proven nor justified. In particular, I have demonstrated that, contrary to its claims, critique [6] has not found any mistakes in my paper [7], or in my other related papers, either in the analytical model for the singlet correlations or in its event-by-event numerical simulations. Moreover, I have brought out a large number of mistakes and incorrect statements from the critique [6] and the critiques it relies on. Some of these mistakes are surprisingly elementary.
GistNoesis 2y ago
The Bell's Inequalities are a test for the capacity for inductive reasoning of the pupil. If the pupil succeed he is not to be admitted to join the ranks of quantum physicist. You usually show a pupil the problem with classical probabilities, and show that you can't violate Bell's Inequalities, then you show that Quantum Mechanics managed to replicated the observed probabilities using a non-local way, and therefore you conclude that the world is non-local. But this logic doesn't stand. You need to use inductive reasoning to see it through. Ask yourself the question, what change would it take to your theory to make it local and still replicate the observed probabilities (and still look reasonable). Solve the riddle (it's quite beautiful once you see it :) ) and you will be rewarded with the awesome title of crackpot physicist, pitted against other dubious crackpot physicist each convinced their loopholes are the ones and only.
- gus_massa 2y ago
  > and therefore you conclude that the world is non-local. No, Bell's inequality has a few sensible assumtions, like locality. The conclusion is that at least one of them is wrong and real world is a sensible one :(. By the way, there is this crazy thing call QM that nobody likes but gives accurate results.
  - GistNoesis 2y ago
    Just because there is a way, doesn't make it the only way. >but gives accurate results. Giving accurate results is missing the point. Hint: The point is understanding how nature's does it. Here is the Chesterton's fence implied by Bell's Inequality : Lemma: There exist a local classical simulator that allows to simulate a universe that behaves according to the probabilities of QM. Corollary : we can simulate "fast" a universe which behaves (in law) exactly like our universe. Nota Bene : This doesn't mean we can compute QM probabilities fast, (we can't), although one way of computing them would be to use Montecarlo estimation on various instances of universe simulations. The question is not whether to lift the fence, or how to lift the fence, the question is how are numerical biological instabilities handled.
    - 2y ago
Strilanc 2y ago
If you want to try your hand at violating Bell inequalities, there are widgets in [1] that allow you to input strategies (as javascript) for Alice and Bob. It continuously performs Monte Carlo sampling of the strategies and presents their success rate. There's a classical-only widget, that goes through quite some contortions behind the scenes to prevent cheating via writing to global variables, and a quantum-allowed widget where that kind of cheating is possible due to the underlying implementation cheating in precisely that using-globals way in order to correctly simulate the quantum mechanics. Anyways, I've had a few people tell me playing around with the widgets helped them understand the inequality. [1]: https://algassert.com/quantum/2015/10/11/Bell-Tests-vs-No-Communication.html https://algassert.com/quantum/2015/10/11/Bell-Tests-vs-No-Co...
tsimionescu 2y ago
> This is known as a Bell inequality. It captures the essential limitation imposed by any theory based on local hidden variables — theories that adhere to classical notions of determinism (no random chance in the measurement apparatus), locality (no faster-than-light influences) and realism (pre-existing properties). Obligatory reminder that there is an extra assumption here: the assumption that the result of the coin flip is not correlated to the hidden state of the particle. If when receiving a particle in stage a_H your coin flip always leads to, say, HH, then you will break Bell's inequality even if all the other assumptions hold. Theories that have this property are called "superdeterministic".
jmmcd 2y ago
This was really excellent - for many of us, code helps to make mechanisms concrete, and it forces every single thing to be pinned down, and not hand-waved away. (Like another commenter, I was also hoping for a direct/standalone explanation for why the red matrix is transposed.)
westurner 2y ago
Hidden variable theory: https://en.wikipedia.org/wiki/Hidden-variable_theory https://en.wikipedia.org/wiki/Hidden-variable_theory Bell test: https://en.wikipedia.org/wiki/Bell_test https://en.wikipedia.org/wiki/Bell_test : > To do away with this assumption it is necessary to detect a sufficiently large fraction of the photons. This is usually characterized in terms of the detection efficiency η [\eta], defined as the probability that a photodetector detects a photon that arrives at it. Anupam Garg and N. David Mermin showed that when using a maximally entangled state and the CHSH inequality an efficiency of η > 2*sqrt(2)/2~= 0.83 is required for a loophole-free violation.[51] Later Philippe H. Eberhard showed that when using a partially entangled state a loophole-free violation is possible for η>2/3~=0.67 which is the optimal bound for the CHSH inequality.[53] Other Bell inequalities allow for even lower bounds. For example, there exists a four-setting inequality which is violated for η>(sqrt(5)-1)/2~=0.62 [54] CHSH inequality: https://en.wikipedia.org/wiki/CHSH_inequality https://en.wikipedia.org/wiki/CHSH_inequality /sbin/chsh Isn't it possible to measure the wake of a photon instead of measuring the photon itself; to measure the wake without affecting the boat that has already passed? And shouldn't a simple beam splitter be enough to demonstrate entanglement if there is an instrument with sufficient sensitivity to infer the phase of a passed photon? This says that intensity is sufficient to read phase: https://news.ycombinator.com/item?id=40492160 https://news.ycombinator.com/item?id=40492160 : > "Bridging coherence optics and classical mechanics: A generic light polarization-entanglement complementary relation" (2023) https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.033110 https://journals.aps.org/prresearch/abstract/10.1103/PhysRev... : >> This means that hard-to-measure optical properties such as amplitudes, phases and correlations—perhaps even these of quantum wave systems—can be deduced from something a lot easier to measure: light intensity And all it takes to win the game is to transmit classical bits with digital error correction using hidden variables?
- westurner 2y ago
  From "Violation of Bell inequality by photon scattering on a two-level emitter" https://news.ycombinator.com/item?id=40917761 https://news.ycombinator.com/item?id=40917761 ... From "Scientists show that there is indeed an 'entropy' of quantum entanglement" (2024) https://news.ycombinator.com/item?id=40396001#40396211 https://news.ycombinator.com/item?id=40396001#40396211 : > IIRC I read on Wikipedia one day that Bell's actually says there's like a 60% error rate?(!) That was probably the "Bell test" article, which - IIUC - does indeed indicate that if you can read 62% of the photons you are likely to find a loophole-free violation. What is the photon detection rate in this and other simulators?
axilmar 2y ago
> Victor can prepare a pair of quantum particles in a special state known as an entangled state. In this state, the outcomes of Alice's and Bob's measurements are not just random but are correlated in a way that defies any classical explanation based on local hidden variables. What if there are no hidden properties per particle, but the combination of specific property values of particles allow for breaking Bell's Inequality? I.e. what we call 'entanglement', it might not be 'action-at-a-distance', but the simple effect of the interaction of the properties of the two particles as they are generated. For example, if we have two billiard balls, which are really close together, and we hit them with a third ball simultaneously, their spin will be correlated when we measure it for both balls (without taking into account other factors, i.e. friction, tilting of the table etc). Wouldn't that break Bell's inequality as well? the spins of the two balls will be correlated.
- Maro 2y ago
  "their spin will be correlated" - in this case the billiard's spin is a per-ball property that is set before they are sent to Alice and Bob, and happens to be correlated. You can simulate this in the Python code, but you will not be able to break the Bell inequality like that. This is similar to the dice example I give, where the objects sent to Alice and Bob are random from their perspective (since the dice roll happens with Victor), and correlated. In general, classical correlation cannot break the Bell inequalities [assuming no peeking, ie. no action-at-a-distance in the measurement devices]. To be clear, I didn't prove this in the article, the approach the article takes is "here is some code, play around with it to get a feeling for why". Hope this helps.
  - axilmar 2y ago
    > In general, classical correlation cannot break the Bell inequalities [assuming no peeking, ie. no action-at-a-distance in the measurement devices]. What if the particles have properties that mutate their state after they are sent to Alice and Bob? Suppose, in the billiards example, that I put a small device into the balls that changes the spin of the ball to some predefined value. Wouldn't that break the Bell inequalities without action at a distance? The reason for the breaking would be that the state of the balls would be modified after they are sent to Alice and Bob. It would look like action at a distance without being 'action at a distance'.
antognini 2y ago
Incidentally, there is a variant of the canonical Bell experiment called the Greenberger-Horne-Zeilinger (GHZ) experiment that doesn't require multiple trials to collect statistics. The GHZ experiment uses three photons in an entangled state rather than two and can produce a result that is incompatible with classical mechanics in just a single observation. https://en.wikipedia.org/wiki/GHZ_experiment https://en.wikipedia.org/wiki/GHZ_experiment
- Strilanc 2y ago
  It's impossible produce a result incompatible with classical mechanics in a single constant-sized observation, because the classical players can get any result by just playing randomly. The advantage that GHZ has, similar to the Mermin-Peres magic square game, is that the quantum players should win 100% of the time while classical players win less than 90% of the time. This gives much faster Bayesian updates away from classical mechanics towards quantum mechanics as you collect samples (compared to CHSH). But you do still need multiple samples. On the other hand, seeing the GHZ game fail would be instant total loss for quantum mechanics. If the win rate is supposed to be 100%, and you see a loss (that you can't attribute to noise or something), then in that case a single test would have caused you to totally discount quantum mechanics.

122 points by Maro 2y ago

anxcna 2y ago

[flagged]

kzrdude 2y ago
Why not use numpy's rng?
fancyfredbot 2y ago
In which way is python's random module broken, specifically?
jgalt212 2y ago
I would assume the secrets standard library creation might be related to this concern. https://docs.python.org/3/library/secrets.html https://docs.python.org/3/library/secrets.html

danwills 2y ago

"a talented college physics student can do it" I'm afraid I don't qualify for being able to do that, but I feel like I'm tantalizingly close to understanding this overall - but I'm finding it hard to understand why the lower-right "TT" quadrant is transposed in the S=2.828 example (the red box in the diagram). Maybe it's obvious if one understands it better?

n4r9 2y ago
It requires a chunk of linear algebra to understand, but the Wikipedia page has a slightly more detailed explanation: https://en.wikipedia.org/wiki/Bell%27s_theorem#Theorem https://en.wikipedia.org/wiki/Bell%27s_theorem#Theorem It's related to the fact that the expected value of A_1 tensor B_1 is negative 1/sqrt(2), whilst the expected value of all other tensor products are positive 1/sqrt(2).
- jahnu 2y ago
  The explanation and table in the Simple English page for this helped me grasp it better. (Although the diagram using green dots only confuses :) ) Greene's book is a fantastic read too! https://simple.wikipedia.org/wiki/Bell%27s_theorem https://simple.wikipedia.org/wiki/Bell%27s_theorem
  - gus_massa 2y ago
    > Although the diagram using green dots only confuses :) It's very confusing. In particular it does not say that the box have 3 doors until the middle of the explanations. Also, I don't find the example very similar to the Bell's Inequality. Moreover, I expect in a quantum system that when both open the same door they get the same result (or the oposite) so in a quantum system I expect that when both open the same door they get 100% (or 0%) agreement, so insted of 50% I expect 1/3 * 100% + 2/3 * 50 % = 66% (or 1/3 * 0% + 2/3 * 50 % = 33%). Anyway, in some versions of the Bell's Inequality the doors of the boxes are "misalignment" so on box has white-gray-black doors and the other has another ser of colors. let's say creme-pink-brown doors. You never have a 100% or 0% of coincidences of the results.
  - n4r9 2y ago
    This looks like some kind of variant of Bell's Theorem. I've not seen it before, but it reminds me of the GHZ inequality [0] [[EDIT - actually I take that back. The GHZ inequality refers to three systems whereas your link refers to three measurement choices]]. I don't think your link gives a derivation of the quantum correlations beyond "Quantum physics says that half the time they should get a match". [0] https://en.wikipedia.org/wiki/Bell%27s_theorem#GHZ%E2%80%93Mermin_(1990) https://en.wikipedia.org/wiki/Bell%27s_theorem#GHZ%E2%80%93M...
Maro 2y ago
Hi, I'm the guy who wrote the article. In the article, I first show how to "break" the Bell inequality without making a reference to any complicated math or Physics, this is the section "Breaking the Bell inequality with non-local information", which uses the dice roll example. This is on purpose, for pedagogical reasons, and this is why the Python approach imo is so useful to demonstrate this whole thing: the key idea is, to break the inequality, you need to "peek" at the other side. Then, the next mental step is simply the statement that, in "real life", you can prepare a composite system (eg. 2 photons modeled as 2 qubits) that you can seperate (modeled as the split() function in Python), you can send the 2 parts to two different observers, they use a certain measurement setup, and the whole game is played, statistic computed, etc. and then you get this value 2.82 (which breaks the Bell inequality)! So somehow, the 2 qubits are doing that we can only model [in Python] as peeking! The actual derivation of how to get that 2.82 is, in some sense, almost like a a detail. I think with this approach, even a non-physicist can understand what this whole argument is (=Bell's genius). "a talented college physics student can do it" - I'm a Physicist, but I'm not working as a Physicist, and I was able to derive all the numbers in that table by hand with pen & paper directly. I figured if I can do it 15 years out of school, so can a talented college physics student! The next article will be that derivation [of the raw probabilities], I just need to transcribe it from my notebook to Latex and clean it up. If you want to see the original notes: https://photos.app.goo.gl/sqxLnEhyeZTDD7oA6 https://photos.app.goo.gl/sqxLnEhyeZTDD7oA6

n4r9 2y ago

This is closely related to my PhD. It was many years ago but if I remember rightly there is no need for the assumption of determinism - Bell Inequalities hold just as well for random local hidden variables. Simulating the correlations with computer programs is an interesting idea, partly because it challenges to those who still believe in a "local" reality to demonstrate Bell Inequality violations in distributed classical computer systems. Back in the day there was a crackpot researcher named Joy Christian who kept publishing repetitive papers in the belief that geometric algebras provided a counterexample (it looks like he's still going strong! [0]). Of course, there's nothing about geometric algebras that cannot be modelled in a computer program, so in principle Christian should have been able to demonstrate Bell violations in a distributed scenario. Needless to say, this hasn't happened even though it would be a momentous breakthrough in the foundations of physics. [0] https://ieeexplore.ieee.org/document/9693502 https://ieeexplore.ieee.org/document/9693502

eigenket 2y ago
You know something has gone horrifically badly when a paper begins with > This reply paper should be read as a continuation of my previous reply paper [1], which is a reply published in this journal to a previous critique of one of my papers We're way too deep in replies now, and anyone who values their time should get out now.
- 0cf8612b2e1e 2y ago
  On the other hand, academics slap fights are magnificently petty to behold. In any dispute the intensity of feeling is inversely proportional to the value of the issues at stake. That is why academic politics are so bitter.
  - n4r9 2y ago
    The conclusion reads like someone who can't admit they're wrong on Reddit: > The common defect in the critiques [2], [6], and [14] is that, instead of engaging with the original quaternionic 3-sphere model presented in my papers [1], [7]– [11] using Geometric Algebra, they insist on criticizing entirely unrelated flat space models based on matrices and vector “algebra.” This logical fallacy by itself renders the critiques invalid. Nevertheless, in this paper I have addressed every claim made in the critique [6] and the critiques it relies on, and demonstrated, point by point, that none of the claims made in the critiques are correct. I have demonstrated that the claims made in the critique [6] are neither proven nor justified. In particular, I have demonstrated that, contrary to its claims, critique [6] has not found any mistakes in my paper [7], or in my other related papers, either in the analytical model for the singlet correlations or in its event-by-event numerical simulations. Moreover, I have brought out a large number of mistakes and incorrect statements from the critique [6] and the critiques it relies on. Some of these mistakes are surprisingly elementary.

GistNoesis 2y ago

The Bell's Inequalities are a test for the capacity for inductive reasoning of the pupil. If the pupil succeed he is not to be admitted to join the ranks of quantum physicist. You usually show a pupil the problem with classical probabilities, and show that you can't violate Bell's Inequalities, then you show that Quantum Mechanics managed to replicated the observed probabilities using a non-local way, and therefore you conclude that the world is non-local. But this logic doesn't stand. You need to use inductive reasoning to see it through. Ask yourself the question, what change would it take to your theory to make it local and still replicate the observed probabilities (and still look reasonable). Solve the riddle (it's quite beautiful once you see it :) ) and you will be rewarded with the awesome title of crackpot physicist, pitted against other dubious crackpot physicist each convinced their loopholes are the ones and only.

gus_massa 2y ago
> and therefore you conclude that the world is non-local. No, Bell's inequality has a few sensible assumtions, like locality. The conclusion is that at least one of them is wrong and real world is a sensible one :(. By the way, there is this crazy thing call QM that nobody likes but gives accurate results.
- GistNoesis 2y ago
  Just because there is a way, doesn't make it the only way. >but gives accurate results. Giving accurate results is missing the point. Hint: The point is understanding how nature's does it. Here is the Chesterton's fence implied by Bell's Inequality : Lemma: There exist a local classical simulator that allows to simulate a universe that behaves according to the probabilities of QM. Corollary : we can simulate "fast" a universe which behaves (in law) exactly like our universe. Nota Bene : This doesn't mean we can compute QM probabilities fast, (we can't), although one way of computing them would be to use Montecarlo estimation on various instances of universe simulations. The question is not whether to lift the fence, or how to lift the fence, the question is how are numerical biological instabilities handled.
  - 2y ago

Strilanc 2y ago

If you want to try your hand at violating Bell inequalities, there are widgets in [1] that allow you to input strategies (as javascript) for Alice and Bob. It continuously performs Monte Carlo sampling of the strategies and presents their success rate. There's a classical-only widget, that goes through quite some contortions behind the scenes to prevent cheating via writing to global variables, and a quantum-allowed widget where that kind of cheating is possible due to the underlying implementation cheating in precisely that using-globals way in order to correctly simulate the quantum mechanics. Anyways, I've had a few people tell me playing around with the widgets helped them understand the inequality. [1]: https://algassert.com/quantum/2015/10/11/Bell-Tests-vs-No-Communication.html https://algassert.com/quantum/2015/10/11/Bell-Tests-vs-No-Co...

tsimionescu 2y ago

> This is known as a Bell inequality. It captures the essential limitation imposed by any theory based on local hidden variables — theories that adhere to classical notions of determinism (no random chance in the measurement apparatus), locality (no faster-than-light influences) and realism (pre-existing properties). Obligatory reminder that there is an extra assumption here: the assumption that the result of the coin flip is not correlated to the hidden state of the particle. If when receiving a particle in stage a_H your coin flip always leads to, say, HH, then you will break Bell's inequality even if all the other assumptions hold. Theories that have this property are called "superdeterministic".

jmmcd 2y ago

This was really excellent - for many of us, code helps to make mechanisms concrete, and it forces every single thing to be pinned down, and not hand-waved away. (Like another commenter, I was also hoping for a direct/standalone explanation for why the red matrix is transposed.)

westurner 2y ago

Hidden variable theory: https://en.wikipedia.org/wiki/Hidden-variable_theory https://en.wikipedia.org/wiki/Hidden-variable_theory Bell test: https://en.wikipedia.org/wiki/Bell_test https://en.wikipedia.org/wiki/Bell_test : > To do away with this assumption it is necessary to detect a sufficiently large fraction of the photons. This is usually characterized in terms of the detection efficiency η [\eta], defined as the probability that a photodetector detects a photon that arrives at it. Anupam Garg and N. David Mermin showed that when using a maximally entangled state and the CHSH inequality an efficiency of η > 2*sqrt(2)/2~= 0.83 is required for a loophole-free violation.[51] Later Philippe H. Eberhard showed that when using a partially entangled state a loophole-free violation is possible for η>2/3~=0.67 which is the optimal bound for the CHSH inequality.[53] Other Bell inequalities allow for even lower bounds. For example, there exists a four-setting inequality which is violated for η>(sqrt(5)-1)/2~=0.62 [54] CHSH inequality: https://en.wikipedia.org/wiki/CHSH_inequality https://en.wikipedia.org/wiki/CHSH_inequality /sbin/chsh Isn't it possible to measure the wake of a photon instead of measuring the photon itself; to measure the wake without affecting the boat that has already passed? And shouldn't a simple beam splitter be enough to demonstrate entanglement if there is an instrument with sufficient sensitivity to infer the phase of a passed photon? This says that intensity is sufficient to read phase: https://news.ycombinator.com/item?id=40492160 https://news.ycombinator.com/item?id=40492160 : > "Bridging coherence optics and classical mechanics: A generic light polarization-entanglement complementary relation" (2023) https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.033110 https://journals.aps.org/prresearch/abstract/10.1103/PhysRev... : >> This means that hard-to-measure optical properties such as amplitudes, phases and correlations—perhaps even these of quantum wave systems—can be deduced from something a lot easier to measure: light intensity And all it takes to win the game is to transmit classical bits with digital error correction using hidden variables?

westurner 2y ago
From "Violation of Bell inequality by photon scattering on a two-level emitter" https://news.ycombinator.com/item?id=40917761 https://news.ycombinator.com/item?id=40917761 ... From "Scientists show that there is indeed an 'entropy' of quantum entanglement" (2024) https://news.ycombinator.com/item?id=40396001#40396211 https://news.ycombinator.com/item?id=40396001#40396211 : > IIRC I read on Wikipedia one day that Bell's actually says there's like a 60% error rate?(!) That was probably the "Bell test" article, which - IIUC - does indeed indicate that if you can read 62% of the photons you are likely to find a loophole-free violation. What is the photon detection rate in this and other simulators?

axilmar 2y ago

> Victor can prepare a pair of quantum particles in a special state known as an entangled state. In this state, the outcomes of Alice's and Bob's measurements are not just random but are correlated in a way that defies any classical explanation based on local hidden variables. What if there are no hidden properties per particle, but the combination of specific property values of particles allow for breaking Bell's Inequality? I.e. what we call 'entanglement', it might not be 'action-at-a-distance', but the simple effect of the interaction of the properties of the two particles as they are generated. For example, if we have two billiard balls, which are really close together, and we hit them with a third ball simultaneously, their spin will be correlated when we measure it for both balls (without taking into account other factors, i.e. friction, tilting of the table etc). Wouldn't that break Bell's inequality as well? the spins of the two balls will be correlated.

Maro 2y ago
"their spin will be correlated" - in this case the billiard's spin is a per-ball property that is set before they are sent to Alice and Bob, and happens to be correlated. You can simulate this in the Python code, but you will not be able to break the Bell inequality like that. This is similar to the dice example I give, where the objects sent to Alice and Bob are random from their perspective (since the dice roll happens with Victor), and correlated. In general, classical correlation cannot break the Bell inequalities [assuming no peeking, ie. no action-at-a-distance in the measurement devices]. To be clear, I didn't prove this in the article, the approach the article takes is "here is some code, play around with it to get a feeling for why". Hope this helps.
- axilmar 2y ago
  > In general, classical correlation cannot break the Bell inequalities [assuming no peeking, ie. no action-at-a-distance in the measurement devices]. What if the particles have properties that mutate their state after they are sent to Alice and Bob? Suppose, in the billiards example, that I put a small device into the balls that changes the spin of the ball to some predefined value. Wouldn't that break the Bell inequalities without action at a distance? The reason for the breaking would be that the state of the balls would be modified after they are sent to Alice and Bob. It would look like action at a distance without being 'action at a distance'.

antognini 2y ago

Incidentally, there is a variant of the canonical Bell experiment called the Greenberger-Horne-Zeilinger (GHZ) experiment that doesn't require multiple trials to collect statistics. The GHZ experiment uses three photons in an entangled state rather than two and can produce a result that is incompatible with classical mechanics in just a single observation. https://en.wikipedia.org/wiki/GHZ_experiment https://en.wikipedia.org/wiki/GHZ_experiment

Strilanc 2y ago
It's impossible produce a result incompatible with classical mechanics in a single constant-sized observation, because the classical players can get any result by just playing randomly. The advantage that GHZ has, similar to the Mermin-Peres magic square game, is that the quantum players should win 100% of the time while classical players win less than 90% of the time. This gives much faster Bayesian updates away from classical mechanics towards quantum mechanics as you collect samples (compared to CHSH). But you do still need multiple samples. On the other hand, seeing the GHZ game fail would be instant total loss for quantum mechanics. If the win rate is supposed to be 100%, and you see a loss (that you can't attribute to noise or something), then in that case a single test would have caused you to totally discount quantum mechanics.