Convex polytopes and quantum separability

We advance a perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose a criterium based on the consideration of convex subsets of quantum states. This criterium generalizes a property of product states to convex subsets (of the set of quantum states) that is able to uncover an interesting geometrical property of the separability property.