Determination of hidden variable models reproducing the spin-singlet

TL;DR

This paper characterizes hidden-variable models that replicate quantum predictions for spin singlets while respecting free will and no-signaling, expanding understanding of quantum foundations.

Contribution

It identifies the form of hidden-variable models compatible with quantum mechanics for spin singlets, satisfying free will and no-signaling, and provides a method to construct many such models.

Findings

Two classes of models are explicitly constructed.

A general recipe for infinitely many models is provided.

Models reproduce quantum predictions while respecting key hypotheses.

Abstract

The experimental violation of Bell inequality establishes necessary but not sufficient conditions that any theory must obey. Namely, a theory compatible with the experimental observations can satisfy at most two of the three hypotheses at the basis of Bell's theorem: free will, no-signaling, and outcome-Independence. Quantum mechanics satisfies the first two hypotheses but not the latter. Experiments not only violate Bell inequality, but show an excellent agreement with quantum mechanics. This fact restricts further the class of admissible theories. In this work, the author determines the form of the hidden-variable models that reproduce the quantum mechanical predictions for a spin singlet while satisfying both the hypotheses of free will and no-signaling. Two classes of hidden-variable models are given as an example, and a general recipe to build infinitely many possible models is provided.