Separability of heterogeneous multipartite quantum systems using Bloch Vectors

Abstract

Refining recent results, we propose an upper bound for the norms of Bloch Vectors for heterogeneous quantum systems containing an arbitrary number of qudits with possibly different numbers of levels. We also generalize recent approaches for tripartite and four-partite heterogeneous systems and for multipartite homogeneous systems. Our results imply a necessary algebraic condition for separability of a general multipartite heterogeneous quantum system under arbitrary partitioning.