Characterization of distillability of entanglement in terms of positive maps

Abstract

A necessary and sufficient condition for 1-distillability is formulated in terms of decomposable positive maps. As an application we provide insight into why all states violating the reduction criterion map are distillable and demonstrate how to construct such maps in a systematic way. We establish a connection between a number of existing results, which leads to an elementary proof for the characterisation of distillability in terms of 2-positive maps.

arXiv comment4 pages, revtex4. Published revised version, title changed, expanded discussion, main result unchanged

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• Positive maps and entanglement in real Hilbert spaces
• Positive tensor products of qubit maps and n-tensor-stable positive qubit maps
• The Jamiołkowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number $k$ and $k$-positive maps
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
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• Ground State Instabilities and Entanglement in the Detuned Dicke Model
• New Partial Trace Inequalities and Distillability of Werner States
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• Dualities and positivity in the study of quantum entanglement