Conditional entropies and their relation to entanglement criteria

Karl Gerd H. Vollbrecht; Michael M. Wolf

doi:10.1063/1.1498490

Conditional entropies and their relation to entanglement criteria

Karl Gerd H. Vollbrecht
, Michael M. Wolf

Technische Universität Braunschweig

Research output: Contribution to journal › Article › peer-review

64 Scopus citations

Abstract

We discuss conditional Rényi and Tsallis entropies for bipartite quantum systems of finite dimension. We investigate the relation between the positivity of conditional entropies and entanglement properties. It is in particular shown that any state having a negative conditional entropy with respect to any value of the entropic parameter is distillable since it violates the reduction criterion. Moreover, we show that the entanglement of Werner states in odd dimensions can neither be detected by entropic criteria nor by any other spectral criterion.

Original language	English
Pages (from-to)	4299-4306
Number of pages	8
Journal	Journal of Mathematical Physics
Volume	43
Issue number	9
DOIs	https://doi.org/10.1063/1.1498490
State	Published - 1 Sep 2002
Externally published	Yes

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10.1063/1.1498490

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AB - We discuss conditional Rényi and Tsallis entropies for bipartite quantum systems of finite dimension. We investigate the relation between the positivity of conditional entropies and entanglement properties. It is in particular shown that any state having a negative conditional entropy with respect to any value of the entropic parameter is distillable since it violates the reduction criterion. Moreover, we show that the entanglement of Werner states in odd dimensions can neither be detected by entropic criteria nor by any other spectral criterion.

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DO - 10.1063/1.1498490

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Conditional entropies and their relation to entanglement criteria

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