Note on genuine multipartite classical correlations

TL;DR

This paper examines the coexistence of quantum and classical multipartite correlations, proposing a new definition for genuine classical correlations and analyzing existing measures like covariance.

Contribution

It introduces a postulate for measures of genuine multipartite classical correlations and demonstrates that covariance does not satisfy this postulate.

Findings

Covariance does not satisfy the proposed postulate.

A new definition for genuine multipartite classical correlations is proposed.

Examples illustrate the new definition.

Abstract

We discuss the problem of coexistence of genuine quantum multipartite correlations and classical multipartite correlations. We introduce a postulate which any measure of genuine multipartite classical correlations should satisfy. We show that covariance does not satisfy this postulate. Finally we propose a definition of genuine multipartite correlations and illustrate it with examples.