Quantum Dissension: Generalizing Quantum Discord for Three-Qubit States

TL;DR

This paper introduces quantum dissension, a new measure of quantum correlations in three-qubit systems, generalizing quantum discord to multipartite states and revealing unique properties like negativity.

Contribution

It defines quantum dissension using three-variable mutual information and explores its properties and implications for three-qubit states, including GHZ and W states.

Findings

Quantum dissension can be negative, unlike quantum discord.

Measurement on a subsystem can enhance correlations in the system.

Multiple definitions of dissension depend on measurement types.

Abstract

We introduce the notion of quantum dissension for a three-qubit system as a measure of quantum correlations. We use three equivalent expressions of three-variable mutual information. Their differences can be zero classically but not so in quantum domain. It generalizes the notion of quantum discord to a multipartite system. There can be multiple definitions of the dissension depending on the nature of projective measurements done on the subsystems. As an illustration, we explore the consequences of these multiple definitions and compare them for three-qubit pure and mixed GHZ and W states. We find that unlike discord, dissension can be negative. This is because measurement on a subsystem may enhance the correlations in the rest of the system. This approach can pave a way to generalize the notion of quantum correlations in the multiparticle setting.