A multipartite generalization of quantum discord

TL;DR

This paper introduces a multipartite quantum discord that generalizes the bipartite concept, measures total non-classical correlations, and relates to monogamy and bipartite contributions in tripartite systems.

Contribution

It proposes a consistent multipartite quantum discord that extends the bipartite definition and decomposes into bipartite and tripartite correlation contributions.

Findings

The multipartite discord is zero only for classically correlated systems.

It decomposes into bipartite and tripartite contributions.

The bipartite part is non-negative and measures non-classical correlations.

Abstract

A generalization of quantum discord to multipartite systems is proposed. A key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems. It is by construction zero only for systems with classically correlated subsystems and is a non-negative quantity, giving a measure of the total non-classical correlations in the multipartite system with respect to a fixed measurement ordering. For the tripartite case, we show that the discord can be decomposed into contributions resulting from changes induced by non-classical correlation breaking measurements in the conditional mutual information and tripartite mutual information. The former gives a measure of the bipartite non-classical correlations and is a non-negative quantity, while the latter is related to the monogamy of the non-classical correlations.