Spectral Conditions for Positive Maps

We provide partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes the celebrated Choi example of a map which is positive but not completely positive. It is shown how the spectral conditions enable one to cons...

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Bibliographic Details
Published in:Communications in mathematical physics 2009-09, Vol.290 (3), p.1051-1064
Main Authors: Chruściński, Dariusz, Kossakowski, Andrzej
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:We provide partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes the celebrated Choi example of a map which is positive but not completely positive. It is shown how the spectral conditions enable one to construct linear maps on tensor products of matrix algebras which are positive but only on a convex subset of separable elements. Such maps provide basic tools to study quantum entanglement in multipartite systems.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-009-0790-8