I am currently trying to understand Bell's Theorem in Quantum Mechanics, and I have been wondering if the following interpretation would fall under the local realism / hidden variables.

Consider an entangled quantum state for two particles, and assign it a cryptographic hash (or something indistinguishable from random). Now the two particles go their own way, and get measured. Let's assume that the collapse of the state during the measurement involves pseudo-random based on the common hash as random seed and the measurement itself. This pseudo-random would be indistinguishable from true random for observers, and could follow the usual quantum mechanics, nothing changed there. We only tweaked the dices so to speak. However since both particles share the hash, their pseudo-random would not be completely independent, it could for instance "carry" indirect information about certain states. The "same" measurement would give coherent results for instance, like opposed spins.

Does the above hash fall under the "Hidden Variables"? At first it does look like a hidden variable, but it does not fall under the usual definition of a classic variable (like position, speed, mass... etc), and neither does its use, since it is not in determining probabilities or possibilities, but in the outcome of the dice throw.

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    $\begingroup$ Yeah, this is just a hidden variable theory, but you've made the hidden variables more complicated. Hidden variable just means "each particle just carries some local information", which can mean a number, a coin flip result, or a seed. Bell's theorem applies to all of them. $\endgroup$ – knzhou Feb 18 '16 at 17:14
  • $\begingroup$ I made a lot of hard simulations starting from this idea. I found weird results : good emulation if we take in account the lost particles during the experiment. I don't answer because always downvoted on a subject ( a soap ) not well understood by many. To answer your question ( it was mine too ) , the answer is no ! It's not consistent with hidden variables fixed at their generation time or else you enter in another controversy on the experiment settings $\endgroup$ – user46925 Feb 18 '16 at 17:36
  • $\begingroup$ @knzhou after further enquiries, while it is definitely local, it may not be realist. As the pseudo-random generation only takes place during observation, there is no defined state before the measurement, and no reality separate from observation. The spanner however is that a prng would be too chaotic and unable to reproduce entanglement with just a shared seed, it could require the measure to be quantisized "just so it works" $\endgroup$ – Eric Grange Feb 18 '16 at 20:17
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    $\begingroup$ Bell kind of falls apart at the seams quickly when you know about path integrals. A path integral is basically a hidden variable theory that reproduces quantum mechanics correctly. It is non-local, just as you would expect, it has a beautiful physical interpretation, just as you would expect from something that Dirac and Feynman came up with and it is two things that Bell is not: 1) It's actually science and 2) It's actually useful. $\endgroup$ – CuriousOne Feb 18 '16 at 23:42
  • $\begingroup$ @CuriousOne Bell requires both locality and realism. The million dollars question seems to be which of locality or realism is incorrect, as they are undermined by QM experimental results. Both could be incorrect as well. $\endgroup$ – Eric Grange Feb 19 '16 at 8:55

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