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.