Polygamy relation of quantum correlations with equality

TL;DR

This paper introduces a generalized framework for quantum correlation polygamy relations with equality, providing new inequalities and demonstrating their applicability to various quantum measures and multipartite systems.

Contribution

It presents a novel polygamy relation with equality using polygamy weights, applicable to any quantum correlation measure and multipartite states.

Findings

Derived polygamy inequalities for the $eta$th power of quantum correlation measures

Illustrated the relations using concurrence of assistance

Extended relations to quantum entanglement measures not satisfying traditional polygamy inequalities

Abstract

We provide a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy relation with equality, we present polygamy inequalities satisfied by the $\beta$th $(\beta>0)$ power of the quantum correlation measures. Taking concurrence of assistance as an example, we further illustrate the significance and advantages of these relations. We also obtain a polygamy relation with equality by considering the one-to-group entanglements for any quantum entanglement measures that do not satisfy the polygamy relations. We demonstrate that such relations for tripartite states can be generalized to multipartite systems.