A new parameterized monogamy relation between entanglement and equality

TL;DR

This paper introduces a generalized, parameterized monogamy relation for entanglement measures, transforming the traditional inequality into an equality, and explores its implications for various quantum systems.

Contribution

It proposes a new monogamy equality based on monogamy weight, extending the understanding of entanglement distribution in quantum systems.

Findings

Monogamy relations can be expressed as equalities rather than inequalities.

The relations are applicable to the $ ext{α}$th power of entanglement measures.

Multiple copies of states can recover monogamy relations for non-additive measures.

Abstract

We provide a generalized definition of the monogamy relation for entanglement measures. A monogamy equality rather than the usual inequality is presented based on the monogamy weight, from which we give monogamy relations satisfied by the $\alpha$th $(\alpha>0)$ power of the entanglement measures. Taking concurrence as an example, we further demonstrate the significance and advantages of these relations. In addition, we show that monogamy relations can be recovered by considering multiple copies of states for every non-additive entanglement measure that violates the inequalities. We also demonstrate that the such relations for tripartite states can be generalized to multipartite systems.