Hidden-variable hypothesis in quantum paradoxes

Aleksandr V. Belinskii

Van der Merwe, Alwyn, Gino Tarozzi

Dagomir Kaszlikowski, Marek Żukowski

We show the series of Greenberger-Horne-Zeilinger-like paradoxes for N maximally entangled N-dimensional quantum systems. The hypothesis of local hidden variables leads to a prediction of perfect correlations that do not appear for the quantum systems.

Jaykov Foukzon, Менькова Елена Романовна, Alexander A Potapov

Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.

Shahen Hacyan

Yakir Aharonov, Daniel Rohrlich