Classification of mixed three-qubit states

Phys Rev Lett. 2001 Jul 23;87(4):040401. doi: 10.1103/PhysRevLett.87.040401. Epub 2001 Jul 3.


We introduce a classification of mixed three-qubit states, in which we define the classes of separable, biseparable, W, and Greenberger-Horne-Zeilinger 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.