Hidden Variables, Joint Probability, and the Bell Inequalities

TLDR

The Bell inequalities hold. The paper demonstrates that a quantum correlation experiment admits a deterministic hidden‑variables model, a factorizable stochastic model, a single joint distribution for all observables, and well‑defined joint distributions for all pairs and triples of commuting and non‑commuting observables, showing these statements are mutually equivalent.

Abstract

It is shown that the following statements about a quantum correlation experiment are mutually equivalent. (1) There is a deterministic hidden-variables model for the experiment. (2) There is a factorizable, stochastic model. (3) There is one joint distribution for all observables of the experiment, returning the experimental probabilities. (4) There are well-defined, compatible joint distributions for all pairs and triples of commuting and noncommuting observables. (5) The Bell inequalities hold.