Bloch vector norms of separable multi-partite quantum systems

Abstract

In this letter, we find an upper bound for the norms of Bloch vectors for quantum systems comprised of an arbitrary number of qudits. We generalize a recent result of Li et al. for four-partite quantum systems. We apply our result to provide an upper bound on the entanglement measure given by the Bloch vector norm and we provide a necessary algebraic condition for separability of a general multi-partite quantum system under any arbitrary partition function. Finally we show that the finer the partitioning is, the smaller our upper bound becomes.