Abstract:
Our main aim in this paper is to inform the physics community (and
especially experts in quantum information) about investigations of
the problem of the probabilistic compatibility of a family of random
variables: the possibility of realizing such a family based on a single
probability measure (of constructing a single Kolmogorov probability
space). These investigations were started a hundred years ago by Boole.
The complete solution of the problem was obtained by the Soviet mathematician
Vorobiev in the 1960s. It turns out that probabilists and statisticians
obtained inequalities for probabilities and correlations that include
the famous Bell's inequality and its generalizations.
Keywords:
Bell's inequality, nonlocality, “death of reality”, probabilistic incompatibility of random variables, Boole's necessary condition, Vorobiev theorem, contextual description of the EPR–Bohm experiment.
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