  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 {\bf 63}, 022104 (2001)]} is larger than 1/2 for mixed multipartite
systems of an arbitrary dimension.
