Bell inequalities as constraints on unmeasurable correlations

TL;DR

This paper revisits Bell inequalities, showing they can be viewed as constraints on unmeasurable correlations that are compatible with quantum mechanics in certain cases, challenging traditional interpretations of nonlocality.

Contribution

It demonstrates that Bell inequalities can be understood as conditions on unmeasurable correlations, linking classical representability to the structure of quantum correlations.

Findings

Bell inequalities relate to the intersection of unmeasurable correlation ranges

Compatibility with quantum predictions depends on the structure of observable relations

Classical representations are possible for certain sets of correlations

Abstract

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations < A_i >, < B >, < A_i B >, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation < A_1 A_2 > associated to different choices for B. The same analysis applies to the Hardy model and to the "perfect correlations" discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality.