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I would like to apologize if this is the wrong StackExchange site but I couldn't think of anything better.

I'm writing my thesis about random number generators. In a section about quantum random number generators I'm trying to explain on a high level why they are random and what guarantees their randomness. I was wondering if I could make the following statement:

Any physical effect that violates Bell-CHSH inequality is fundamentally quantum in nature. Because quantum effects are indeterministic their outcomes cannot be predicted and are great sources of randomness.

From what I understand, Bell-CHSH inequality can be used to prove that hidden local variables theory doesn't explain QM and QM is, in fact, not classic. However can I extend this logic to conclude that any kind of physical effect violating those inequalities is quantum/non-classic as well?

Ideally I'd love to get some citations I can quote even if I'm wrong. I majored in CS and proving this is probably way over me.

I can translate the whole part of my thesis should it be relevant.

EDIT: Added the local part of "hidden local variables" and changed my wording. Thanks @Wolphram jonny

EDIT 2:

If it helps anything then my train of thought was as follows:

  1. QM was proven to be not classic by Bell's inequality violations
  2. Quantum effects were proven to be random/unpredictable
  3. Someone thought it would be a good idea to create an RNG based on quantum effects
  4. ME: If some physical effect violates Bell's inequality we can conclude it's quantum in nature.

It looks like I'm missing a proof for 2. and 4.

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  • $\begingroup$ The inequality does not discard hidden variables theories, only "local" hidden variable theories. In any case, a violation of the inequalities only shows that QM is not classical, not that it is truly random. But we do believe that QM measurements behave in an undistinguishable way from truly random, so in principle we believe it is a good source of randomness. $\endgroup$ – Wolphram jonny Jan 17 at 0:52
  • $\begingroup$ @Wolphramjonny right, I forgot the local part, my bad. I have corrected the question. Am I correct assuming that there are no direct proof for quantum effects being random? $\endgroup$ – Michał Zając Jan 17 at 0:59
  • $\begingroup$ I would say the last statement is correct, but you/I would likely want to hear more opinions, that is why I would not put it as an answer. $\endgroup$ – Wolphram jonny Jan 17 at 1:03
  • $\begingroup$ This is even more complicated that I initially thought. My line of reasoning was as follows: We found out that QM is not classic by breaking Bell's theorem -> It was proven that quantum effects are fundamentally random/unpredicatable -> someone thought it's a good idea to create a random number generator out of that -> If something's breaking Bell's theorem then it's fundamentally quantum in effect. $\endgroup$ – Michał Zając Jan 17 at 1:06
  • $\begingroup$ 1. right 2. you cannot prove a theory in physics, only perform experiments that are in agreement with it until you find one that does not.3.right, because we believe QM behaves randomly for all curent practical purposes 4. That is false, there might be an infinite number of non classical theories that violate the inequalities, not just QM $\endgroup$ – Wolphram jonny Jan 17 at 3:48
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I'm not sure whether this is exactly what you are asking, but I would say that observing the violation of a Bell's inequality certifies (under a few assumptions) that the observations cannot be explained by a classical model.

On the other hand, quantum mechanics does correctly predict outcomes that violate said inequalities.

I think it's a bit tricky to say that this implies that the effects are quantum in nature. Rather, it shows that the observed effects are compatible with the predictions of quantum mechanics, but not those of classical physics. Whether this is enough to say that the physical effects are quantum in nature is mostly a matter of interpretation of the sentence.

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  • $\begingroup$ I see, thank you! I ended up with the following statement which I believe has no falsehoods until someone comes up with a theory that's better than QM. „Violations of Bell-CHSH inequalites experimentally prove that behavior of an entangled state cannot be explained by classical model. All experiments up to date suggest that quantum effects are fundamentally random, and, therefore, are a good source of randomness.” $\endgroup$ – Michał Zając Jan 18 at 18:41

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