Szilárd Szalay, Zoltán Kökényesi
We extend the classification of mixed states of quantum systems composed by arbitrary number of subsystems of arbitrary dimensions. This extended classification turns out to be complete in the sense of partial separability and gives 1+18+1 partial separability classes in the three-partite case contrary to the known 1+8+1. We also give necessary and sufficient criteria for the classes by the use of convex roof extensions of functions defined on pure states. In the special case of three-qubit systems, we define a different set of such functions by the help of the Freudenthal triple system approach of three-qubit entanglement.
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http://arxiv.org/abs/1206.6253
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