Hidden-variable models for the spin singlet. II. Local theories violating Bell and Leggett inequalities

TL;DR

This paper presents local hidden-variable models that violate Bell and Leggett inequalities but do not match quantum predictions, highlighting limitations of these inequalities in capturing quantum nonlocality.

Contribution

It introduces three classes of local hidden-variable models violating Bell and Leggett inequalities without reproducing quantum results, challenging their completeness.

Findings

Models violate Bell and Leggett inequalities

Models do not reproduce quantum predictions

Outcome independence and locality are uncorrelated

Abstract

Three classes of local hidden-variable models that violate both Bell and Leggett inequalities are presented. The models, however, do not reproduce the quantum mechanical predictions, hence they are experimentally testable. It is concluded that on one hand neither Bell or Leggett inequality fully captures the essential counterintuitiveness of quantum mechanics, while on the other hand the hypothesis of outcome independence and that of locality are uncorrelated.