Bell's Inequalities and the issue of non-locality

[Tolga T]

TL;DR Summary

This year's Nobel Prize goes to the esteemed experimenters who showed beyond doubt that QM satisfies Bell's inequalities. Among the claimed implications of this result is that physics is essentially non-local. This is the point on which I like to raise doubts.

QM is compatible with Bell's inequalities clearly shows that no deterministic program can give similar results for entangled particles. In other words, there is no deterministic algorithm that mimics QM that the particles already follow before the measurement. So far, so good. But of course, this does not exclude that there can be a non-deterministic algorithm that the particles obey already before the measurement. After all, that is what QM is all about. In pairs of entangled particles, each particle has its own right to be measured at a particular time at a particular place in the entire universe. Experimenting with such a particle would not yield any surprising results other than that it obeys QM.

To speculate more about this, consider the following: spin is a conserved quantity. Thus, the entanglement process creates two particles spinning (so to speak) in the opposite direction. Therefore, as expected, any measurement on the same axis will always give opposite results (no need for spooky action !). The particles are also equipped with wave functions (and with spin operators) that are set so that the results of experiments at different locations comply with the Bell Inequalities. Also here there is no necessity for remote action.

I know this is too simplistic and superficial, and probably suffers from a lack of deeper understanding. I would appreciate any comments.

 

[Nugatory]

QM is compatible with Bell's inequalities clearly shows that no deterministic program can give similar results for entangled particles.

That’s exactly backwards. QM is INcompatible with Bell’s inequality: Quantum mechanics predicts that under some circumstances the inequality will be violated; experiments have confirmed the QM prediction; therefore no alternative theory that predicts that the inequality is never violated can be correct.

To speculate more about this, consider the following: spin is a conserved quantity. Thus, the entanglement process creates two particles spinning (so to speak) in the opposite direction. Therefore, as expected, any measurement on the same axis will always give opposite results (no need for spooky action !). The particles are also equipped with wave functions (and with spin operators) that are set so that the results of experiments at different locations comply with the Bell Inequalities. Also here there is no necessity for remote action.

That is exactly the sort of explanation that Bell proved is impossible. It is not possible to “set” the properties of the particles in such a way that the inequality is violated in the way that QM predicts.
Aside from about 93 bazillion threads here at Physics Forums, you will find this paper and this website (maintained by a member here) to be helpful.

 

[Tolga T]

Thank you for your reply and the links. Sorry for my language, I did not reference the Bell inequalities correctly. Let me try to rephrase it:
- That Bell's inequalities are (sometimes) violated is a fact of nature.
- If I get it right, hidden variables (Bell's reality) are deterministic by construction. Therefore, it is certainly not possible to deterministically specify the properties of particles in a way that violates Bell's inequalities and QM predicts this.
- But I can not see why particles can have stochastic built-in processes that sometimes violate Bell and predict QM. Why can not hidden variables be random variables?

 

[vanhees71]

Thank you for your reply and the links. Sorry for my language, I did not reference the Bell inequalities correctly. Let me try to rephrase it:
- That Bell's inequalities are (sometimes) violated is a fact of nature.

The history is as follows: Bell formulated a class of hidden-variable theories that he called "local and realistic", which implies an inequality for the statistical outcomes of certain measurements, which contradict the predictions for these statistical outcomes due to quantum theory.

Among others, the 2022-physics-nobel-prize laureats have experimentally tested Bell's local realistic hidden-variable theories and quantum theory to decide which prediction is right. As expected, quantum theory is right with an amazing statistical significance, and local realistic hidden-variable theories fail with the same statistical significance.

- If I get it right, hidden variables (Bell's reality) are deterministic by construction. Therefore, it is certainly not possible to deterministically specify the properties of particles in a way that violates Bell's inequalities and QM predicts this.

"Reality" in Bell's sense means the assumption that all observables always take predetermined values, and the statistical nature of the outcomes of measurements are due to the ingnorance on the values of the hidden variables.

QT assumes that there's no state of any quantum system, where all observables take determined values. This is quantified by the Heisenberg uncertainty relations for incompatible observables.

- But I can not see why particles can have stochastic built-in processes that sometimes violate Bell and predict QM. Why can not hidden variables be random variables?

The point is realism, i.e., the assumption that all observables always take determined values, no matter whether we (can) know these values or not. You can say: According to QT Nature is inherently stochastic, i.e., the randomness of the outcomes of measurements does not originate from our ignorance of the values the observables have before measurement but from the impossibility to prepare a state where all observables take determined values.

 

[PeroK]

- But I can not see why particles can have stochastic built-in processes that sometimes violate Bell and predict QM. Why can not hidden variables be random variables?

Essentially those are non-local variables, which Bell's Theorem does not rule out.

However, here's the real issue. We have a theory of QM that predicted the value of spin or polarization measurements before the experiments were possible. When the experiments were conducted, the results precisely matched the QM predictions. Essentially, that's as much as you can ask of a scientific theory.

Why are we certain it's not something else and it only looks like QM is correct? We aren't certain. That's not the way science works. Until some experiment goes against QM predictions, the theory holds.

The alternative is to assume there is some unknown theory (as yet undiscovered) that has stochastic hidden processes that just happen to replicate the outcomes predicted by QM. And one probably could be constructed mathematically. But, unless and until that theory is more precisely specified and predictions different from QM are produced, then what is the purpose of it?

There is another idea called superdeterminism, which has the similar idea of replacing QM with an as yet unspecified alternative that just happens to make it look like QM is correct. Here's Scott Aaronson's view on this:

https://scottaaronson.blog/?p=6215

 

[Tolga T]

The alternative is to assume there is some unknown theory (as yet undiscovered) that has stochastic hidden processes that just happen to replicate the outcomes predicted by QM. And one probably could be constructed mathematically. But, unless and until that theory is more precisely specified and predictions different from QM are produced, then what is the purpose of it?

This is exactly my point. Such a theory would save locality, i.e., one need not worry about universal wave functions or instantaneous correlations at a distance. On the other hand, I also doubt why and how such a theory would make different (or better) predictions than QM.

 

[PeroK]

This is exactly my point. Such a theory would save locality,

Such a theory is fundamentally non-local, as the stochastic processes between separated particles must be correlated. And, correlated to precisely match QM predictions, without actually being QM.

Locality is ruled out by the violations of Bell's Theorem.

 

[DrChinese]

- But I can not see why particles can have stochastic built-in processes that sometimes violate Bell and predict QM. Why can not hidden variables be random variables?

Well, Bell proves that is not possible. And without understanding the Bell proof, it will be difficult to accept that. I will humbly point you to one of my web pages that may assist in this:

https://drchinese.com/David/Bell_Theorem_Easy_Math.htm
"No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics"

However, you may be able to understand the issue in this manner:

1. For your "stochastic" method to work, there must be "answers" to measurements on spin/polarization entangled particles at any angle selected by an observer (say Alice) - regardless of the measurement performed by a second observer (say Bob). Yet, if they happen to select the same angle to perform their measurements, their results must be perfectly correlated (or anti-correlated depending on the type of entanglement). Agree?

2. Imagine Alice and Bob measure correlated photons only at 0, 120, or 240 degrees. According to QM, when they measure at the same angle, the result is 100% matching. When measuring at different angles, the difference (usually termed "theta") is always 120 degrees. The quantum prediction for this is cos^2(theta) which for a difference of 120 degrees is matches=25%. Agree?

3. Suppose you can't think up a good algorithm for you stochastic process. No problem, I'll let you cheat! You can pick the outcomes yourself by hand so that everything works out!! That way, you can prove that Bell is wrong. I've started a list for you, you can complete it (and keep in mind the outcomes for Alice and Bob must match at the same angles):

Alice : Bob
0/120/240 : 0/120/240
Y / N / Y : Y / N / Y
N / Y / Y : N / Y / Y
[ you place a bunch of examples here ]4. Oops! There is no way to hand pick outcomes such that the average of matches - when the angles are different - is 25% (what QM predicts and experiments actually show). Your average will always be no lower than 1 in 3 (33%) - no matter how you do it. For each of the 2 examples I presented, the average is exactly 1/3 (YN, YY, YN and NY, NY, YY is 2 matches and 4 mismatches, averaging 2/6 which is 1/3). The point is: The quantum matching prediction is only a function of theta, and nothing else. There can be no stochastic functions that work as you imagine, you have now demonstrated that.

 

[PeterDonis]

Why can not hidden variables be random variables?

Randomness by itself doesn't help you, because randomness by itself can't produce the kinds of correlations we observe. You would just get a bunch of random, uncorrelated results.

Also, randomness is not required. The Bohmian interpretation of QM has completely deterministic hidden variables--the particle positions--but their dynamics is explicitly nonlocal--the wave function that guides the particle positions updates itself instantaneously over the entire universe. This nonlocality is how the Bohmian model is able to violate the Bell inequalities and match the predictions of QM.

 

[LittleSchwinger]

The point is realism, i.e., the assumption that all observables always take determined values, no matter whether we (can) know these values or not.

To the OP this is the reason for violations of Bell's Inequality in quantum mechanics. To prove Bell's inequality you assume that all observables take well-defined values (realism) and that locality holds. Determinism isn't assumed. So if you make a theory that's stochastic but is still local and realist it won't be enough.

Quantum Theory breaks the former assumption of realism¹.

If you want to have a theory where all observables take well-defined values, you need to give up the second condition: locality. This is done in other formalisms like Bohmian Mechanics, but these other formalisms currently can't handle the majority of modern physics.

¹Don't get too hung up on the name. Saying quantum theory is "non-realist" is a technical phrase meaning not all observables take well-defined values at all times.

 

[Tolga T]

Well, Bell proves that is not possible. And without understanding the Bell proof, it will be difficult to accept that. I will humbly point you to one of my web pages that may assist in this:

https://drchinese.com/David/Bell_Theorem_Easy_Math.htm
"No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics"

However, you may be able to understand the issue in this manner:

1. For your "stochastic" method to work, there must be "answers" to measurements on spin/polarization entangled particles at any angle selected by an observer (say Alice) - regardless of the measurement performed by a second observer (say Bob). Yet, if they happen to select the same angle to perform their measurements, their results must be perfectly correlated (or anti-correlated depending on the type of entanglement). Agree?

2. Imagine Alice and Bob measure correlated photons only at 0, 120, or 240 degrees. According to QM, when they measure at the same angle, the result is 100% matching. When measuring at different angles, the difference (usually termed "theta") is always 120 degrees. The quantum prediction for this is cos^2(theta) which for a difference of 120 degrees is matches=25%. Agree?

3. Suppose you can't think up a good algorithm for you stochastic process. No problem, I'll let you cheat! You can pick the outcomes yourself by hand so that everything works out!! That way, you can prove that Bell is wrong. I've started a list for you, you can complete it (and keep in mind the outcomes for Alice and Bob must match at the same angles):

Alice : Bob
0/120/240 : 0/120/240
Y / N / Y : Y / N / Y
N / Y / Y : N / Y / Y
[ you place a bunch of examples here ]4. Oops! There is no way to hand pick outcomes such that the average of matches - when the angles are different - is 25% (what QM predicts and experiments actually show). Your average will always be no lower than 1 in 3 (33%) - no matter how you do it. For each of the 2 examples I presented, the average is exactly 1/3 (YN, YY, YN and NY, NY, YY is 2 matches and 4 mismatches, averaging 2/6 which is 1/3). The point is: The quantum matching prediction is only a function of theta, and nothing else. There can be no stochastic functions that work as you imagine, you have now demonstrated that.

Thank you for your detailed and crystal-clear explanation. I cannot help but raise the following:

- Measurements at the same angle cannot be part of a random process. It is not a stochastic process because the outcome is known with certainty. Therefore, no stochastic process can fit all the data together.

- Also, these measurements should not be counted as contributing to the correlation. Consider the random variables X (1 or 0) and Y (1 or 0), which denote the outcome of the experiments at different sites. Experimenters at each site are free to choose angles 0,120 and 240 degrees with equal probability. Once a stream of data has been collected from X and Y, the portion of the data that was due to the same angles and the rest are samples from completely different processes, one deterministic and the other stochastic.

- I like to think of the deterministic process as a physical process that occurs in the process of entanglement (like two balls spinning in opposite directions to conserve the angular momentum).

- The second process is a physical stochastic process that arises in the very same process of entanglement.

As for Bell's assumptions, my main concern is localism, not realism. Correlations are real and unavoidable, but a correlation in itself does not always require a cause-effect relationship. There can be (are) physical processes that produce correlations. I find a universal wave function (controlling distant events simultaneously (whatever that means!)) as in pilot wave theory or with entangled particles in a physical world quite hard to digest.

 

[Nugatory]

Correlations are real and unavoidable, but a correlation in itself does not always require a cause-effect relationship.

Well, of course not - that’s the generally accepted explanation for how entangled particles displaying opposite spins does not violate special relativity.

I find a universal wave function (controlling distant events simultaneously (whatever that means!)) as in pilot wave theory or with entangled particles in a physical world quite hard to digest.

Fortunately for you then, you don’t have to try. “Controlling” is not part of the mathematical basis of quantum mechanics, but rather a claim implied by some interpretations. You may find that choosing a different interpretation resolves your digestive difficulties.

 

[Nugatory]

Also, these measurements should not be counted as contributing to the correlation. Consider the random variables X (1 or 0) and Y (1 or 0), which denote the outcome of the experiments at different sites. Experimenters at each site are free to choose angles 0,120 and 240 degrees with equal probability. Once a stream of data has been collected from X and Y, the portion of the data that was due to the same angles and the rest are samples from completely different processes, one deterministic and the other stochastic.

Yes, that is an example of how a non-local theory¹ can produce results that violate Bell’s inequality, and therefore is consistent with Bell’s theorem². If that is your point I’m not sure why you’re making it - you and Bell are in violent agreement.

Footnotes:
1) Any theory that considers different processes when the detectors are aligned and not aligned is non-local - need to know the settings of both detectors to predict what happens at one detector.
2) Bell’s theorem and Bell’s inequality are different things. The theorem says that any theory that violates the inequality is necessarily non-local or non-realistic.

 

[vanhees71]

At this point I have to stress once more that there is a "standard explanation" within the mundane "minimal statistical interpretation" of relativistic quantum field theory (or within the Standard Model of particle physics): From this point of view physics (quantum as well as the classical approximations) is local in the sense that space-like separated events cannot be causally connected, i.e., the measurement on one piece of an entangled system cannot causally affect any measurement on another far-distant piece of this system (e.g., two entangled photons, being measured at far-distant places), i.e., if the "detection events" are space-like separated according to standard relativistic QFT, there cannot be any causal influence between these measurements. This is built into standard relativistic QFT by assuming the socalled microcausality constraint according to which operators representing local observables must commute at space-like separated arguments.

The observed correlations due to entanglement are thus to be understood as properties of these entangled states, which the system has due to the preparation of the system in this state before the measurements to reveal them were done.

As Einstein once put it in his amazing clarity: It's not so much the apparent "faster-than-light influcences" which seem to follow from naive collapse assumptions of some flavors of Copenhagen interpretations, that bothered him, but the "inseparability" of far-distant entangled parts of quantum systems. Unfortunately neither the profound importance of the microcausality constraint nor Bell's discovery of the incompatibility between "local realistic HV models" and "quantum (field) theory") where known during Einstein's lifetime. It would be very interesting to know, how Einstein would have reacted when learning that indeed there is relativistic microcausal QFT, which is in accordance with the causality structure of relativity as well as the violation of Bell's inequality, predicted by it, ruling out "local realistic HV theories", and that thus at least in the minimal interpretation of Q(F)T this indicates that one has to rule out "realism", i.e., that not all observables take determined values, and that thus the statistical nature of the outcome of measurements is "objective" and not just due to our "ignorance of the values of some hidden variables".

 

[Fra]

ruling out "local realistic HV theories", and that thus at least in the minimal interpretation of Q(F)T this indicates that one has to rule out "realism", i.e., that not all observables take determined values, and that thus the statistical nature of the outcome of measurements is "objective" and not just due to our "ignorance of the values of some hidden variables".

How about this simple example, thay may not be perfect but still illustrate a subtle point in bells ansatz, the equipartition ansatz, where the "interactions" are statistically summed as per the HV. I argue that this ansatz can be questionable without necessarily dumping the whole idea of a hidden variable in the first place.

About the expectation of values on the stock market, there may exist hidden variables (inside information) that _if revealed_ to the market, would influence the expectations. If all the actors on the marker would know about the hidden variable - except for one player, this player could probably come up with an expectation (similar to the ansatz in bells theorem) to simply average all the possible values, based on the (to him) unknown inside HV.

But of course, the actual expectation values on the market would not follow this expectation is NO actor has this information. Ie. the "companys inside info" is isolated from the environment. Ie. any insiders are kept isolated from the market interactions even if the company said "split" into two. This is what happens in a quantum interaction. It does not imply that there is no hidden variables, it only implies that hidden variables does not affect decision makers as long as they are kept unknown.

What is the difference betwee the scenarios? I would say it has to do with HOW the expectations of actors are FORMED (ie the "hamiltonians"). Actors does not react to facts that are hidden, they react only to available information to them. And there are information that is public, and there is information that is available to say only two isolated parts. In the latter cases it influences the reaction of those parts on the environment only; once released from isolation.

Thus IMO Bells theorem specifically proves that the idea that only the physicists is "ignorance" about the outcome, can not explain the quantum interaction. (this is what i calle the "naive" form of the ansatz) But it does not disprove the case where the whole environment is "ignorant" to it. I've never seen this emphasized which I think is strange.

What would be thinkg of hidden inside information in the market, that is never leaked? Is it "real" or not?

/Fredrik

 

[vanhees71]

How about this simple example, thay may not be perfect but still illustrate a subtle point in bells ansatz, the equipartition ansatz, where the "interactions" are statistically summed as per the HV. I argue that this ansatz can be questionable without necessarily dumping the whole idea of a hidden variable in the first place.

Can you specify what you mean in mathematical terms? What do you mean by "equipartition ansatz"?

 

[Fra]

Perhaps I should say to avoid the usual misunderstandings - I didn't exactly disagree to your previous post I just wanted to add one extra reflection considering the OT, and distinguish between from whom or what the HVs are "hidden". Hidden to all, or hidden to some, as from my perspective that is a key distinction.

Can you specify what you mean in mathematical terms? What do you mean by "equipartition ansatz"?

I mean just a normal partitioning of the sample space, I argue that this anzats makes sense in the case where the ignorance refers to a few actors, not all. IF it is hidden to all the ansatz is not obvious to me. And the point is that the entangled pair IS presumable hidden to ALL the environment, not JUST hidden from the physicists. I guess it's just the most simple parts of the ansatz, but I do not think it's trivial.

$$P(A) = \sum_{\lambda} P(A|\lambda)P(\lambda)$$ (this doesnt render right... i cant seem to find the right new syntax)

This ansatz makes sense if there are at least some "agents" or "observers" in the environment that can infer it. But this is hardly the case in the pair production? The market analogy was supposed to give an intuitive handle on this, without getting lost in details (logic tables or other things, which misses the point).

edit: keep forgetting the latex syntx on in the thread

/Fredrik

 

[vanhees71]

The problem with attempts to avoid "getting lost in details" usually leads to misunderstandings, particularly in such a delicate issue as Bell's inequalities.

I think it doesn't matter of the hidden variables are hidden in principle, i.e., referring to possible parameters necessary to describe the system, which in principle can't be known or whether they are just unknown today and may become usual observables when physics makes progress and discovers them. That's the strength of Bell's argument: It's very general, i.e., the only assumption about "local realistic theories" is that there are some additional parameters, which are for whatever reason hidden to us, such that we describe them probabilistically.

Let's take the very clear formulation by Weinberg in his "Lectures on Quantum Mechanics": Realism means that the observables as well as the "hidden variables" always take determined values, i.e., the value of the spin component in direction $\vec{a}$, $s(\vec{a},\lambda)$ is determined by the values of $\lambda$, but we don't know the values of $\lambda$ and assume some probability density $\rho(\lambda)$ (it doesn't matter which $\rho$, it must just obey the usual rules for probability densities). Locality means that $\lambda$ is fixed in the beginning, before the particle decays (assuming we discuss the usual most simple example of the decay of a scalar particle at rest to two spin-1/2 particles). Then all that's needed is that then the expectation values of spin components for the two particles are given by
$$\langle (\vec{a} \cdot \vec{s}_1) (\vec{b} \cdot \vec{s}_2) = \int_G \mathrm{d} \lambda \rho(\lambda) S(\vec{a},\lambda) S(\vec{b},\lambda).$$
Then one can show that with that "local realistic hidden variable model"
$$|\langle (\vec{a} \cdot \vec{s}_1) (\vec{b} \cdot \vec{s}_2)-\langle (\vec{a} \cdot \vec{s}_1) (\vec{c} \cdot \vec{s}_2)| \leq \frac{\hbar^2}{4} + \langle (\vec{b} \cdot \vec{s}_1) (\vec{c} \cdot \vec{s}_2) \rangle,$$
which is violated by the predictions of QT for certain choices of $\vec{a}$ and $\vec{b}$.

Perhaps you can point at the place in this description, where you think one can make different assumptions.

 

[Fra]

The problem with attempts to avoid "getting lost in details" usually leads to misunderstandings, particularly in such a delicate issue as Bell's inequalities

Good point, this is likely to fail again I presume.

I think it doesn't matter of the hidden variables are hidden in principle, i.e., referring to possible parameters necessary to describe the system, which in principle can't be known or whether they are just unknown today and may become usual observables when physics makes progress and discovers them. That's the strength of Bell's argument: It's very general

IMO, Bell's argument is strong and very clear, but narrow. I am not seeking loopholes. I am arguing that Bell's theorem just applies to the most naive form of hidden variables (which are not plausible for me in the first place).

The sort of HV I think of, are rather "subjective variables", one can argue i think that they are very real, they are just not recognised or observable for all observers. Their purpose would not be to restore determinism instead of probability, but to add explanatory value. We know QM predicts things but there is something that keeps these threads coming. There is something about it, that is not satisfactory for some of us.

Let's take the very clear formulation by Weinberg in his "Lectures on Quantum Mechanics": Realism means that the observables as well as the "hidden variables" always take determined values, i.e., the value of the spin component in direction $\vec{a}$, $s(\vec{a},\lambda)$ is determined by the values of $\lambda$
...
Perhaps you can point at the place in this description, where you think one can make different assumptions.

"the value of the spin component in direction, is determined by the values of"

I find this is making subconscious assumptions about intermediate steps in the interactions that is indeed compliant with newtons mechanics (so no surprise it was suggested by Bell), but it does not seem like the only possibility. It does not even seem very plausible in the more modern context of expectation games.

To see why in an intuitive way, I made up the market example as I think anyone can contemplate it. Are the inside information real? Or is not not real because it's hidden?: The conclusion is supposed to be that, the hidden variables can be "real" but not objectively inferrable, and can well explain the "correlation" and save "locality" in every meaningful way, and perhaps a better logic of causal mechanisms (which lacks in QM).

The key question is, how does the rest of the setup (apparatous) interact with the entangled pair, once the isolation is released at the detectors?
$$\langle (\vec{a} \cdot \vec{s}_1) (\vec{b} \cdot \vec{s}_2) = \int_G \mathrm{d} \lambda \rho(\lambda) S(\vec{a},\lambda) S(\vec{b},\lambda).$$

Above suggests that it makes sense to partition the "interaction" according to the HV, regardless of the extent of isolation. I think that partition makes sense only if the extent of isolation (in the environment) is limited to the physicists only. If the reason is not clear, think again about the stock expectation. The key lies in not how any one agent thinks about anything, but in what happens when the expectations of two agents interact. Then I find that thinking about the "solipsist HV" as helpful. And that is not forbidden by Bells theorem.

If this didn't make any sense then skip onto the next post

/Fredrik

 

[James1238765]

Entanglement is real and has been demonstrated in real systems like [this]. Many uses of entanglement (like for quantum communication) don't really require Bell's inequalities to be suspended. Bertlmann's socks entanglement is quite sufficient for some purposes.

Is there an application where EPR-violating entanglement (instead of just Bertlmann socks entanglement) is absolutely crucial for it to work?

 

[PeterDonis]

Many uses of entanglement (like for quantum communication) don't really require Bell's inequalities to be suspended.

I'm not sure where you're getting this from, but AFAIK quantum communication does require Bell inequality violating entanglement, at the very least if you want to prevent eavesdropping.

 

[James1238765]

@PeterDonis Let's take 4 entangled electron pairs created on Earth. Then we take 4 each of the twins to the moon, and leave the other 4 twins on Earth.

Now Alice on Earth wants to send the information 1100. She opens/measures the 4 electron spins, and get the result {0,1,0,1}. So she calls Bob on the moon, and only tells him "the information is same, notsame, notsame, same".

Bob measures his 4 entangled electrons and gets {1,0,1,0}.

Combining this measured spins with Alice's information "same, notsame, notsame, same", Bob reconstructs the entirety of Alice's information: 1100 from his set of entangled electrons.

This whole process does not really require that the spin pairs be undetermined/superpositioned prior to the electrons being separated. (?)

 

[PeterDonis]

@PeterDonis Let's take 4 entangled electron pairs created on Earth. Then we take 4 each of the twins to the moon, and leave the other 4 twins on Earth.

Now Alice on Earth wants to send the information 1100. She opens/measures the 4 electron spins, and get the result {0,1,0,1}. So she calls Bob on the moon, and only tells him "the information is notsame, same, same, notsame".

Bob measures his 4 entangled electrons and gets {1,0,1,0}.

Combining this measures spins with Alice's information "same, notsame, notsame, same", Bob reconstructs the entirety of Alice's information: 1100 from his set of entangled electrons.

You left out the fact that Alice and Bob must both make their measurements with their spin measuring devices in the same orientation. Otherwise the measurements will not be perfectly anticorrelated.

This whole process does not really require that the spin pairs be undetermined/superpositioned prior to the electrons being separated. (?)

The process of sending bits as you describe doesn't even require quantum communication at all, because all you are relying on is perfect anticorrelation between measurements of spin in the same direction, as above. That kind of correlation can be produced classically, and it would be foolish to spend all the extra money on quantum communication just for that.

Actual quantum communication protocols involving cryptography and protection against eavesdropping involve spin measurements at the two ends that are not always in the same direction, and as I understand it, they make use of the fact that correlations between such measurements can violate the Bell inequalities in order to ensure fidelity of transmission.

 

[James1238765]

@PeterDonis Yes, I have read something along the lines. The failure of the Bell test measured at either end will show that the info has been opened somewhere.

It would be nice if someone could give a simple outline of the protocol that achieves this.

 

[James1238765]

@PeterDonis One could also do this as previously, but with a modification, by assigning a number of random extra electrons to be Bell tested. Say, we start with 8 electrons, reserving 4 for information, and 4 for Bell test.

Alice wants to send the information 1100. Right before she wants to communicate with Bob, she randomly rolls a dice and choose to open electron numbers 1, 3, 4, and 8.

Alice measures {0,1,0,1} from these electrons.

She calls Bob and says "the information is same, Bell, notsame, notsame, Bell, Bell, Bell, same". Further communication between them will establish the Bell correlation test numbers on the designated test electrons.

Because which are the test electrons versus which are the information electrons are completely(!) undetermined up to the point (at the last minute) when Alice randomly settles on the information vs test electrons, an eavesdropper will not be able to perfectly predict Alice's choice before she makes them, in order to leave precisely those electrons unopened. So any eavesdropping will collapse the Bell test when Alice and Bob compare their test results.

 

[PeterDonis]

One could also do this as previously, but with a modification, by assigning a number of random extra electrons to be Bell tested.

I don't know that that would be sufficient, since passing the Bell tests on the "Bell" pairs still wouldn't tell you anything about the non-Bell pairs.

You should be looking in the quantum communication literature for descriptions of the protocols. Possibly someone reading this thread will have some useful references. Random speculation is off topic here.

 

[Demystifier]

Why can not hidden variables be random variables?

They can. Hidden variables can be either deterministic or random. What Bell theorem proves is that they can't be local. An example of deterministic hidden variables that reproduce QM is Bohmian interpretation. An example of random hidden variables that reproduce QM is Nelson interpretation. Both Bohmian and Nelson interpretations are non-local. The right story, which is usually not told so, is that Bell was first impressed by non-local Bohmian hidden variables, and then wanted to see whether any hidden variable theory must be non-local, similarly to the Bohmian one. And then he proved (under certain additional reasonable assumptions) that it indeed must.

Later the story was distorted. Most physicists don't like the idea of hidden variables because they can't be measured (that's why they are called "hidden"). So they interpreted the Bell theorem as an argument that hidden variables don't exist, because if they existed they would need to be non-local.

Later later the distorted story above was further distorted, so it turned into a claim that the Bell theorem simultaneously proves non-existence of hidden variables and non-locality of Nature. That's an utter nonsense.

 

[Tolga T]

What happens if the experimenters at sites A and B do not perform the measurements almost simultaneously, but with a time delay, e.g. 5 minutes or 1 day later at site B than at site A? Do such experiments also lead to results that violate Bell's inequalities?

 

[Nugatory]

What happens if the experimenters at sites A and B do not perform the measurements almost simultaneously, but with a time delay, e.g. 5 minutes or 1 day later at site B than at site A? Do such experiments also lead to results that violate Bell's inequalities?

You may be overlooking the relativity of simultaneity here. If the time interval between measurements at the two sites affects whether the inequality is violated, we would find that some observers watching a single run of the experiment will find a violation of the inequality in the results of that run while others looking at the same sequence of measurement results do not. This possibility is difficult to take seriously.

Furthermore these experiments are routinely done with the two measurements spacelike-separated so that not only is the time interval between A’s measurement and B’s measurement not defined, there is no way of saying which came first.

But with that said, there are practical limits to how long we can maintain a pair of particles in a coherent state, and hence to the experiments that have actually been done.

 

[Fra]

Later the story was distorted. Most physicists don't like the idea of hidden variables because they can't be measured (that's why they are called "hidden").

IMO, part of this problem is that the conventional meaning of "measurement" or observables in QM, is what I call an extrinsic measurement. It effectively means that an agent or inside observer that has in fact made a measurement (ie an observation) does not count, unless the whole environment of other agents can confirm it and it all forms an equivalence class. This effectively means that the "measurement results" belongs to the public knowledge, or what we call beeing part of the "classical environment" where we can share information.

I think this is questionable, and it by construction ignores the interaction going among observers [do we want this?] This is also I think related to that the above normal meaning of measurements or observables in QFT, are really only defined relative to a fixed background context where can one repeat interactions to produce statistics.

And I think it's clear that this has it's problems, and one handle I think is rooted already in what physicists normally see as "observable", and thus as demystifier suggests, physicists snorts at any other variables that may be "observable" in a different way and thus has it's place.

/Fredrik

 

[Tolga T]

Furthermore these experiments are routinely done with the two measurements spacelike-separated so that not only is the time interval between A’s measurement and B’s measurement not defined, there is no way of saying which came first.

Of course, the experiments are performed with the two measurements spacelike separated, so one cannot speak of the temporal order of the measurements. However, my hypothetical experiment requires a different setting: perform the measurement events timelike separated (while keeping the particles in a coherent state until the measurements, probably a delay of a tiny fraction of a second would suffice).

 

[Nugatory]

However, my hypothetical experiment requires a different setting: perform the measurement events timelike separated (while keeping the particles in a coherent state until the measurements, probably a delay of a tiny fraction of a second would suffice).

If you mean “a tiny fraction of a second” (as opposed to “5 minutes or 1 day”, which is what you said), then many experiments will qualify.

 

[DrChinese]

1. You may be overlooking the relativity of simultaneity here. If the time interval between measurements at the two sites affects whether the inequality is violated, we would find that some observers watching a single run of the experiment will find a violation of the inequality in the results of that run while others looking at the same sequence of measurement results do not. This possibility is difficult to take seriously.

Furthermore these experiments are routinely done with the two measurements spacelike-separated so that not only is the time interval between A’s measurement and B’s measurement not defined, there is no way of saying which came first.

2. But with that said, there are practical limits to how long we can maintain a pair of particles in a coherent state, and hence to the experiments that have actually been done.

3. However, my hypothetical experiment requires a different setting: perform the measurement events timelike separated (while keeping the particles in a coherent state until the measurements, probably a delay of a tiny fraction of a second would suffice).

1. For spin/polarization tests on entangled pairs: I don't believe there are any frame (relativistic) considerations for the QM predictions. So I would say the Bell inequalities would be violated for all observers. Do you know of any situations otherwise?2. As an interesting aside: It is hard for me to imagine, but coherent storage of of light has been performed for as long as 1 hour. This was not an entangled pair though.

https://www.nature.com/articles/s41467-021-22706-y 3. Yes, you can certainly perform Bell tests in which temporal order is certain (keeping in mind that it makes no difference to the statistical results whether Alice or Bob measures first).

And another experiment which is mind blowing to me: you can entangle 2 photons that have never existed at the same time. One photon is measured by Alice before the Bob photon is even created. (The entanglement itself is created after Alice's measurement, via entanglement swapping.)

https://arxiv.org/abs/1209.4191

 

[vanhees71]

1. For spin/polarization tests on entangled pairs: I don't believe there are any frame (relativistic) considerations for the QM predictions. So I would say the Bell inequalities would be violated for all observers. Do you know of any situations otherwise?

Among the many great achievements by Zeilinger et al. are experiments, where the choice of the measurement setups and registration of two entangled photons were made at space-like separated events (I think in the late 1990ies; I'd have to google to find the corresponding paper(s)).

2. As an interesting aside: It is hard for me to imagine, but coherent storage of of light has been performed for as long as 1 hour. This was not an entangled pair though.

https://www.nature.com/articles/s41467-021-22706-yhttps://www.nature.com/articles/s41467-021-22706-y
https://www.nature.com/articles/s41467-021-22706-y

3. Yes, you can certainly perform Bell tests in which temporal order is certain (keeping in mind that it makes no difference to the statistical results whether Alice or Bob measures first).

And another experiment which is mind blowing to me: you can entangle 2 photons that have never existed at the same time. One photon is measured by Alice before the Bob photon is even created. (The entanglement itself is created after Alice's measurement, via entanglement swapping.)

https://arxiv.org/abs/1209.4191

All this is only mind blowing, if you think that the found correlations between far-distant parts are due to "spooky actions at a distance" and caused by fluences of the different local measurements on these parts. You have to think in terms of microcausal relativistic QFT to realize that such causal influences are not to be expected. As discussed many times before in this forum, the entanglement swapping is possible, because you use entangled pairs, being prepared before manipulating and measuring the various photons involved in these experiments.

The strong correlations between far-distant entangled parts of systems, for which the measured properties on the single part are even maximally uncertain, is a property of the quantum states, i.e., due to the preparation of the systems in these states and not due to "spooky actions at a distance". Of course, you have to give up the idea that there's more to know about the observables than the probabilistic properties described by Q(F)T.

 

[PeroK]

Of course, the experiments are performed with the two measurements spacelike separated, so one cannot speak of the temporal order of the measurements. However, my hypothetical experiment requires a different setting: perform the measurement events timelike separated (while keeping the particles in a coherent state until the measurements, probably a delay of a tiny fraction of a second would suffice).

The fundamental point you are missing is that there is a limit to anti-correlations in classical probability theory. Everything can't be perfectly anti-correlated with everything else. Suppose you have game for three people. Each person tosses a coin. You can have a perfect correlation, where either a) they all gets heads or b) they all get tails. If one of things always happens that's a perfect correlation.

But, you can't have a perfect anti-correlation. If person A gets a Head and person B gets a Tail, then person C must get the same as one of them. Bell's inequality takes this idea further and looks at the maximal possible anti-correlation in the case of electron spin about different axes. If you disagree with Bell's inequality, then you disagree with classical probability theory. Bell's inequality has nothing directly to do with QM.

To get round Bell's inequality is as impossible as having three people toss a coin and all get something different. Assuming the only possibilities are heads and tails. You can have any stochastic process you like, you can have time delays (or not), you can have coins in a "coherent" state or not.

Now, Bell's inequality is not as elementary as the three-coin game, but it is not difficult to prove mathematically.

If you apply Bell's inequality to electron spin, then you assume "realism" (in some sense), locality (in some sense) and classical probability theory. This is Bell's Theorem. If Bell's Theorem fails experimentally (as it does), then you have to give up either realism, locality or classical probability theory (or all three). There is no way round that. Trying to get round that simply means you have not understood Bell's inequality in the first place.

The failure of Bell's theorem is not a problem for QM, because QM predicted it would fail in the first place. Don't underestimate the significance of this and why people who trust QM can't see the issue that others raise. Everything is as predicted by QM, so where's the problem?

The thing you cannot do is pretend that somehow you can get round Bell's inequality and thereby recover realism, locality, and classical variables. That paradigm is gone.