Bell's nonlocality in a general nonsignaling case: quantitatively and conceptually

TL;DR

This paper introduces a generalized probabilistic framework to analyze Bell inequality violations in quantum systems, providing new quantitative measures of nonlocality that challenge traditional interpretations of quantum realism.

Contribution

It develops the LqHV model, a comprehensive probabilistic approach that extends local hidden variable models to accurately describe all nonsignaling quantum correlations.

Findings

Analytical expressions for nonlocality parameters in N-qudit states.

Numerical evaluation of nonlocality parameters for various d and N.

Bell violation attributed to improper HV modeling, not EPR locality violation.

Abstract

Quantum violation of Bell inequalities is now used in many quantum information applications and it is important to analyze it both quantitatively and conceptually. In the present paper, we analyze violation of multipartite Bell inequalities via the local probability model - the LqHV (local quasi hidden variable) model [Loubenets, J. Math. Phys. 53, 022201 (2012)], incorporating the LHV model only as a particular case and correctly reproducing the probabilistic description of every quantum correlation scenario, more generally, every nonsignaling scenario. The LqHV probability framework allows us to construct nonsignaling analogs of Bell inequalities and to specify parameters quantifying violation of Bell inequalities - Bell's nonlocality - in a general nonsignaling case. For quantum correlation scenarios on an N-qudit state, we evaluate these nonlocality parameters analytically in terms of dilation characteristics of an N-qudit state and also, numerically - in d and N. In view of our rigorous mathematical description of Bell's nonlocality in a general nonsignaling case via the local probability model, we argue that violation of Bell inequalities in a quantum case is not due to violation of the Einstein-Podolsky-Rosen (EPR) locality conjectured by Bell but due to the improper HV modelling of "quantum realism".