Classification of mixed high-dimensional multiparticle systems

We present an inequality that classifies mixed multipartite systems of an arbitrary dimension with respect to separability and positivity of partial transpose properties. This inequality gives a way to experimentally classify the observed state of multipartite systems of an arbitrary dimension. The inequality also implies that a sufficient condition for a density operator to have no positive partial transpose with respect to any subsystem is that the fidelity to a generalized Greenberger-Horne-Zeilinger state [A. Cabello, Phys. Rev. A 63, 022104 (2001)] is larger than 1/2 for mixed multipartite systems of an arbitrary dimension.