English

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

Quantum Physics 2009-11-11 v2

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.

Keywords

Cite

@article{arxiv.quant-ph/0509008,
  title  = {On the structure of the body of states with positive partial transpose},
  author = {Stanislaw Szarek and Ingemar Bengtsson and Karol Zyczkowski},
  journal= {arXiv preprint arXiv:quant-ph/0509008},
  year   = {2009}
}

Comments

10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma 3