Classification of mixed three-qubit states

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Abstract
We introduce a classification of mixed three-qubit states, in which we define the classes of separable, biseparable, W- and GHZ-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 zero. We construct witness operators that detect the class of a mixed state. We discuss the conjecture that all entangled states with positive partial transpose (PPTES) belong to the W-class. Finally, we present a new family of PPTES "edge" states with maximal ranks.

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