Quantum dissension: generalizing quantum discord for three-qubit states

Abstract

We introduce the notion of quantum dissension for a three-qubit system as a measure of quantum correlations. We use three classically equivalent expressions of three-variable mutual information. Their differences are 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. Furthermore, when we consider a bipartite split of the system, the dissension reduces to discord. This approach can pave a way to generalize the notion of quantum correlations in the multiparticle setting.