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

Stanisław J Szarek, Ingemar Bengtsson, Karol Życzkowski
2006 Journal of Physics A: Mathematical and General  
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.
doi:10.1088/0305-4470/39/5/l02 fatcat:xeunekfez5gyfoiif6u2u2fkmy