When is a Genuine Multipartite Entanglement Measure Monogamous?

TL;DR

This paper investigates the monogamy properties of genuine multipartite entanglement measures (GMEM), establishing conditions under which they are monogamous and analyzing specific measures like the genuinely multipartite concurrence.

Contribution

It introduces a framework for unified and complete GMEM, proving their monogamy properties and evaluating existing measures within this framework.

Findings

Unified GMEMs are completely monogamous.

Complete GMEMs induced by tightly complete multipartite entanglement measures are tightly complete monogamous.

Genuinely multipartite concurrence is not a suitable GMEM candidate.

Abstract

A crucial issue in quantum communication tasks is characterizing how quantum resources can be quantified and distributed over many parties. Consequently, entanglement has been explored extensively. However, the genuine entanglement still lacks of studying. There are few genuine multipartite entanglement measures and whether it is monogamous is unknown so far. In this work, we explore the complete monogamy of genuine multipartite entanglement measure (GMEM) for which, at first, we investigate a framework for unified/complete GMEM according to the unified/complete multipartite entanglement measure proposed in [Phys. Rev. A 101, 032301 (2020)]. We find a way of inducing unified/complete GMEM from any given unified/complete multipartite entanglement measure.It is shown that any unified GMEM is completely monogamous, and any complete GMEM that induced by some given complete multipartite entanglement measure is tightly complete monogamous whenever the given complete multipartite entanglement measure is tightly complete monogamous. In addition, the previous GMEMs are checked under this framework. It turns out that the genuinely multipartite concurrence is not a good candidate as a GMEM.