Further Results on the Cross Norm Criterion for Separability

Further Results on the Cross Norm Criterion for Separability In the present paper we develop and investigate a novel approach that aims to characterize quantum entanglement by using cross norms. In the first part of the paper we further develop the mathematical theory by determining the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that our techniques induce a novel powerful analytical and computable separability criterion for bipartite systems. This new criterion complements the well-known Peres positive partial transpose criterion in several aspects. It is a necessary but in general not a sufficient criterion for separability. We demonstrate the power of the new criterion by evaluating the criterion for a number of important examples. We also demonstrate that the new criterion is able to detect bound entangled states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Further Results on the Cross Norm Criterion for Separability

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Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer Science+Business Media, Inc.
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-005-5664-1
Publisher site
See Article on Publisher Site

Abstract

In the present paper we develop and investigate a novel approach that aims to characterize quantum entanglement by using cross norms. In the first part of the paper we further develop the mathematical theory by determining the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that our techniques induce a novel powerful analytical and computable separability criterion for bipartite systems. This new criterion complements the well-known Peres positive partial transpose criterion in several aspects. It is a necessary but in general not a sufficient criterion for separability. We demonstrate the power of the new criterion by evaluating the criterion for a number of important examples. We also demonstrate that the new criterion is able to detect bound entangled states.

Journal

Quantum Information ProcessingSpringer Journals

Published: Apr 27, 2005

References

  • A new class of entanglement measures
    Rudolph, O.
  • Conditional entropies and their relation to entanglement criteria
    Vollbrecht, K. G. H.; Wolf, M. M.
  • Entangled quantum systems and the Schmidt decomposition
    Ekert, A.; Knight, P. L.

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