On total correlations in a bipartite quantum joint probability distribution

TL;DR

This paper explores how to decompose total correlations in bipartite quantum distributions into nonlocality, contextuality, and classical parts, introducing measures and analyzing their relationships.

Contribution

It introduces a measure of total correlations and demonstrates additivity relations among nonlocality, contextuality, and classical correlations in quantum systems.

Findings

Quantum correlations satisfy additivity relations among the measures.

Bell discord and Mermin discord are interpreted as distance measures.

A new measure of total correlations divides correlations into classical and nonclassical parts.

Abstract

We discuss the problem of separating the total correlations in a given quantum joint probability distribution into nonlocality, contextuality and classical correlations. Bell discord and Mermin discord which qunatify nonlocality and contextuality of quantum correlations are interpreted as distance measures in the nonsignaling polytope. A measure of total correlations is introduced to divide the total amount of correlations into a purely nonclassical part and a classical part. We show that quantum correlations satisfy additivity relations among these three measures.