On monogamy and polygamy relations of multipartite systems

TL;DR

This paper unifies the understanding of monogamy and polygamy relations of quantum correlations in multipartite systems, showing that these relations extend to other powers of measures and are stronger than previous results.

Contribution

It introduces a unified framework for generalized monogamy and polygamy relations that are transitive to other powers and are demonstrably stronger than existing relations.

Findings

Weighted monogamy and polygamy relations are transitive to other powers.

The new relations are stronger than recent existing ones.

Examples confirm the improved strength of the proposed relations.

Abstract

We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the $r$-power of the measure. We show in a uniformed manner that the generalized monogamy and polygamy relations are transitive to other powers of the measure in weighted forms. We demonstrate that our weighted monogamy and polygamy relations are stronger than recently available relations. Comparisons are given in detailed examples which show that our results are stronger in both situations.