The negativity of partial transpose versus the negativity of Wigner function

Abstract

We investigate the multipartite entanglement in the phase space using the negativity of Wigner function (NWF) and in the Hilbert space using the negativity of partial transpose (NPT). We analyze comparatively these quantities and the different types of entanglements that are present in two major classes — GHZ and [Formula: see text] — made of coherent states. We show that the negativity of Wigner function can be used as a good measure of genuine entanglement in multipartite systems. However, the negativity of partial transpose is a good quantifier for only the bipartite entanglement in tripartite systems.