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On the structure of the body of states with positive partial transpose

Stanislaw Szarek·Ingemar Bengtsson·Karol Zyczkowski
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Abstract

We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random boundary state to be separable, provided the random states are generated uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An analogous property holds for the set of positive-partial-transpose states for an arbitrary bipartite system.

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Stanislaw Szarek, Ingemar Bengtsson, Karol Zyczkowski. 2005-12-02. On the structure of the body of states with positive partial transpose. https://doi.org/10.1088/0305-4470/39/5/l02

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