Unique decompositions, faces, and automorphisms of separable states
| Autor: | Fred Shultz, Erik M. Alfsen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Quantum Physics
Simplex Mathematics::Combinatorics Probability (math.PR) Convex set Mathematics - Operator Algebras FOS: Physical sciences Statistical and Nonlinear Physics State (functional analysis) Automorphism 46N50 (Primary) 46L30 81P68 94B27 (Secondary) Combinatorics Separable state Product (mathematics) FOS: Mathematics Convex combination State space (physics) Operator Algebras (math.OA) Quantum Physics (quant-ph) Mathematical Physics Mathematics - Probability Mathematics |
| Popis: | 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. Since original version:Cor. 6 revised and renamed Thm 6, some definitions added before Cor. 11, introduction revised and references added, typos corrected |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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