Classification of mixed three-qubit states - art. no. 040401

We introduce a classification of mixed three-qubit states, in which we defi ne the classes of separable, biseparable, W, and Greenberger-Horne-Zeilinge r states. These classes are successively embedded into each other. We show that contrary to pure W-type states, the mixed W class is not of measure ze ro. We construct witness operators that detect the class of a mixed state. We discuss the conjecture that all entangled states with positive partial t ranspose (PPTES) belong to the W class. Finally, we present a new family of PPTES "edge" states with maximal ranks.