33 citations · 33 across the 1 of their papers we have counts for
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Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
Stanislaw J. Szarek, Elisabeth Werner, Karol Zyczkowski
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable,…
On the structure of the body of states with positive partial transpose
Stanislaw Szarek, Ingemar Bengtsson, Karol Zyczkowski
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…
Tensor products of convex sets and the volume of separable states on N qudits
Guillaume Aubrun, Stanislaw J. Szarek
This note deals with estimating the volume of the set of separable mixed quantum states when the dimension of the state space grows to infinity. This has been studied recently for…