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We consider the problem of representation of quantum states and observablesin the framework of classical probability theory (Kolmogorov'smeasure-theoretic axiomatics, 1933). Our aim is to show that, in spite of thecommon opinion, correlations of observables $A_1, A_2$ and $B_1,B_2$ involvedin the experiments of the Bohm-Bell type can be expressed as correlations ofclassical random variables $a_1, a_2$ and $b_1, b_2.$ The crucial point is thatcorrelations $\langle A_i, B_j \rangle$ should be treated as conditional on theselection of the pairs $(i, j).$ The setting selection procedure is based ontwo random generators $R_A$ and $R_B.$ They are also considered as observables,supplementary to the "basic observables" $A_1, A_2$ and $B_1, B_2.$ Theseobservables are absent in the standard description, e.g., in the scheme forderivation of the CHSH-inequality. We represent them by classical randomvariables $r_a$ and $r_b.$ Following the recent works of Dzhafarov andcollaborators, we apply our conditional correlation approach to characterize(no-)signaling in the classical probabilistic framework. Consideration theBohm-Bell experimental scheme in the presence of signaling is important forapplications outside quantum mechanics, e.g., in psychology and social science.

Bohm-Bell type experiments: Classical probability approach to (no-)signaling and applications to quantum physics and psychology