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Quantum Information Processing

, Volume 4, Issue 3, pp 241–250 | Cite as

Reversibility of Local Transformations of Multiparticle Entanglement

  • N. Linden
  • S. Popescu
  • B. Schumacher
  • M. Westmoreland
Article

Abstract

We consider the transformation of multisystem entangled states by local quantum operations and classical communication. We show that, for any reversible transformation, the relative entropy of entanglement for any two parties must remain constant. This shows, for example, that it is not possible to convert 2N three-party GHZ states into 3N singlets, even in an asymptotic sense. Thus there is true three-party non-locality (i.e. not all three party entanglement is equivalent to two-party entanglement). Our results also allow us to make quantitative. statements about concentrating multi-particle entanglement. Finally, we show that there is true n-party entanglement for any n.

Keywords

Multiparticle entanglement reversibility local operations relative entropy 

PACS

03.67.-a 

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References

  1. 1.
    Bennett, C. H., Bernstein, H., Popescu, S., Schumacher, B. W. 1996Phys. Rev. A.533824CrossRefGoogle Scholar
  2. 2.
    Bennett, C. H., Popescu, C. H., Rohrlich, D., Smolin, J. A., Thapliyal, A. V. 201)Phys. Rev. A65012307Google Scholar
  3. 3.
    Ohya, M., Petz, D. 1993Quantum Entropy and Its UseSpringer-VerlagBerlinGoogle Scholar
  4. 4.
    Vedral, V., Plenio, M. 1998Phys. Rev. A.571619CrossRefGoogle Scholar
  5. 5.
    M. J. Donald and M. Horodecki, Phys. Lett A. 264. 257 (1999); M. A. Nielsen, Phys. Rev. A. 61. 064301 (2000).Google Scholar
  6. 6.
    K. Audenaert, J. Eisert et al., quant-ph/0103096.Google Scholar
  7. 7.
    Subsequently to the original submission of the manuscript, states for which this is true have been found, see G. Vidal et al., Phys. Rev. Lett. 85. 658 (2000).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • N. Linden
    • 1
  • S. Popescu
    • 2
  • B. Schumacher
    • 3
  • M. Westmoreland
    • 4
  1. 1.Department of MathematicsUniversity of Bristol, University WalkBristolUK
  2. 2.H.H. Wills Physics Laboratory, Hewlett-Packard LaboratoriesUniversity of BristolBristolUK and BRIMS
  3. 3.Department of PhysicsKenyon CollegeGambierUSA
  4. 4.Department of Mathematical SciencesDenison UniversityGranvilleUSA

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