Unique decompositions, faces, and automorphisms of separable states

Details Unique decompositions, faces, and automorphisms of separable states Unique decompositions, faces, and automorphisms of separable states

2009-06-09

arxiv.org/abs/0906.1761v3

Mathematics

Operator Algebras

Since original version:Cor. 6 revised and renamed Thm 6, some definitions added before Cor. 11, introduction revised and refer

Scientific paper

Let S_k be the set of separable states on B(C^m \otimes C^n) admitting a representation as a convex combination of k pure product states, or fewer. If m>1, n> 1, and k \le max(m,n), we show that S_k admits a subset V_k such that V_k is dense and open in S_k, and such that each state in V_k has a unique decomposition as a convex combination of pure product states, and we describe all possible convex decompositions for a set of separable states that properly contains V_k. In both cases we describe the associated faces of the space of separable states, which in the first case are simplexes, and in the second case are direct convex sums of faces that are isomorphic to state spaces of full matrix algebras. As an application of these results, we characterize all affine automorphisms of the convex set of separable states, and all automorphisms of the state space of B(C^m otimes C^n). that preserve entanglement and separability.

Affiliated with

Also associated with

No associations

Rating

Unique decompositions, faces, and automorphisms of separable states does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Unique decompositions, faces, and automorphisms of separable states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unique decompositions, faces, and automorphisms of separable states will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-65339