Entanglement witnesses: construction, analysis and classification

From the physical point of view entanglement witnesses (EWs) define a universal tool for analysis and classification of quantum entangled states. From the mathematical perspective bipartite EWs provide highly non-trivial generalization of positive operators and establish elegant correspondence with...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2014-12, Vol.47 (48), p.483001
Main Authors: Chru ci ski, Dariusz, Sarbicki, Gniewomir
Format: Article
Language:English
Subjects:
entanglement witness
positive maps
quantum entanglement
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Summary:From the physical point of view entanglement witnesses (EWs) define a universal tool for analysis and classification of quantum entangled states. From the mathematical perspective bipartite EWs provide highly non-trivial generalization of positive operators and establish elegant correspondence with the theory of positive maps in matrix algebras. We concentrate on theoretical analysis of various important notions like decomposability, atomicity, optimality, extremality and exposedness. Several methods of construction are provided as well. Our discussion is illustrated by many examples enabling the reader to see the intricate structure of these objects. It is shown that the theory of EWs finds elegant geometric formulation in terms of convex cones and related geometric structures.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/47/48/483001