Abstract
We start with a review on classical probability representations of quantum states and observables. 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 main part of the paper is devoted to the conditional probability model with conditioning on the selection of the pairs of experimental settings. From the viewpoint of quantum foundations, this is a local contextual hidden-variables model. Following the recent works of Dzhafarov and collaborators, we apply our conditional probability approach to characterize (no-)signaling. Consideration of the Bohm–Bell experimental scheme in the presence of signaling is important for applications outside quantum mechanics, e.g., in psychology and social science. The main message of this paper (rooted to Ballentine) is that quantum probabilities and more generally probabilities related to the Bohm–Bell type experiments (not only in physics, but also in psychology, sociology, game theory, economics, and finances) can be classically represented as conditional probabilities.
Highlights
This paper is directed to resolution of the old foundational problem of quantum mechanics: whether it is possible to represent quantum states by classical probability (CP) distributions and quantum observables by random variables [1]
The paper contains a brief review on CP-representations of the probabilistic structure of quantum mechanics
The main part of the paper is devoted to one special CP-representation based on the conditional probability interpretation of quantum probabilities
Summary
This paper is directed to resolution of the old foundational problem of quantum mechanics: whether it is possible to represent quantum states by classical probability (CP) distributions and quantum observables by random variables [1]. We analyze the general measurement scheme involving compatible and incompatible observables which need not be described by the quantum formalism. Our starting point is construction of the CP-representation for quantum mechanics. Throughout the paper, we use capital Latin letters, A, B, R (with indexes) to denote observables and small letters a, b, r (with indexes) to denote classical random variables (RVs)
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