A characterization of optimal entanglement witnesses

Abstract

In this paper, we present a characterization of optimal entanglement witnesses in terms of positive maps and then provide a general method of checking optimality of entanglement witnesses. Applying it, we obtain new indecomposable optimal witnesses which have no spanning property. These also provide new examples which support a recent conjecture saying that the so-called structural physical approximations to optimal positive maps (optimal entanglement witnesses) give entanglement breaking maps (separable states).

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References in corpus (6)

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• Positive finite rank elementary operators and characterizing entanglement of states
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Cited by in corpus (12)

• Entanglement witnesses: construction, analysis and classification
• Optimality for indecomposable entanglement witnesses
• The structural physical approximations and optimal entanglement witnesses
• Necessary and sufficient conditions for local creation of quantum discord
• Entanglement witnesses arising from Choi type positive linear maps
• Entanglement detection beyond the CCNR criterion for infinite-dimensions
• New tools for investigating positive maps in matrix algebras
• Optimal indecomposable witnesses without extremality as well as spanning property
• A class of generalized positive linear maps on matrix algebras
• Entanglement Detection and Distillation for Arbitrary Bipartite Systems
• Optimality of a class of entanglement witnesses for $3\otimes 3$ systems
• Constructing separable states in infinite-dimensional systems by operator matrices