Monogamy deficit for quantum correlation in multipartite quantum system

TL;DR

This paper introduces the concept of monogamy deficit for quantum correlations, providing a unified interpretation and conditions for monogamy inequalities in multipartite quantum systems.

Contribution

It defines monogamy deficit, relates different monogamy inequalities for quantum discord, and establishes conditions for monogamy in tripartite and multipartite states.

Findings

Relation connecting two types of monogamy inequalities for quantum discord.

Unified physical interpretation of monogamy deficits.

Necessary and sufficient conditions for monogamy inequalities in tripartite and multipartite states.

Abstract

We introduce the concept of monogamy deficit for quantum correlation by combining together two types of monogamy inequalities depending on different measurement sides. For tripartite pure state, we demonstrate a relation which connects two types of monogamy inequalities for quantum discord and provide the difference between them. By using this relation, we obtain an unified physical interpretation for these two monogamy deficit. In addition, we find an interesting fact that there is a general monogamy condition for several quantum correlations for tripartite pure states. We then provide a necessary and sufficient condition for the establishment of one kind of monogamy inequality for tripartite mixed state and generalize it to multipartite quantum state.