Entanglement Polygon Inequalities for A Class of Mixed States

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.