Uniqueness of the EPR--chemeleon model

TL;DR

This paper proves the uniqueness of a classical deterministic model that reproduces EPR correlations while respecting causality and locality, establishing it as the sole such model under natural assumptions.

Contribution

It demonstrates that any local causal probability measure reproducing EPR correlations must be identical to the previously constructed model, confirming its uniqueness.

Findings

The model reproduces EPR correlations without ad hoc procedures.

Any local causal measure matching EPR correlations coincides with the model.

The proof establishes the model's uniqueness under natural assumptions.

Abstract

A classical deterministic, reversible dynamical systems, reproducing the Einstein--Podolsky--Rosen (EPR) correlations in full respect of causality and locality and without the introduction of any ad hoc selection procedure, was constructed in the paper [AIR02]. In the present paper we prove that the above mentioned model is unique (see Theorem (2) in the sense that any local causal probability measure which reproduces the EPR correlations must coincide, under natural and generic assumptions, with the one constructed in [AIR02]. [AIR02] L. Accardi, K. Imafuku and M. Regoli, "ON THE EPR--CHAMELEON EXPERIMENT", Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 5 (2002) 1--20.