Entanglement Polygon Inequalities for A Class of Mixed States

TL;DR

This paper extends entanglement polygon inequalities to a specific class of mixed states derived from generalized W-class states, introducing tighter bounds and a bipartite relation using Tsallis-q entanglement.

Contribution

It is the first to analyze entanglement polygon inequalities for mixed states in higher dimensions, proposing tighter inequalities and a bipartite relation.

Findings

Mixed states satisfy entanglement polygon inequalities with Tsallis-q entanglement.

Tighter inequalities for mixed states are proposed.

An inequality relating bipartite entanglement for these mixed states is derived.

Abstract

The study on the entanglement polygon inequality of multipartite systems has attracted much attention. However, most of the results are on pure states. Here we consider the property for a class of mixed states, which are the reduced density matrices of generalized W-class states in multipartite higher dimensional systems. First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement, then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement. At last, we get an inequality for the mixed states, which can be regarded as a relation for bipartite entanglement.