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Necessary and Sufficient Condition for Greenberger-Horne-Zeilinger Diagonal States to Be Full N-partite Entangled

  • Koji Nagata
Article

Abstract

We show that any N-qubit state which is diagonal in the Greenberger-Horne-Zeilinger basis is full N-qubit entangled state if and only if no partial transpose of the multiqubit state is positive with respect to any partition.

Keywords

Entanglement Quantum information theory 

References

  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000) MATHGoogle Scholar
  2. 2.
    Galindo, A., Martín-Delgado, M.A.: Rev. Mod. Phys. 74, 347 (2002) CrossRefADSGoogle Scholar
  3. 3.
    Bell, J.S.: Physics (Long Island City, N.Y.) 1, 195 (1964) Google Scholar
  4. 4.
    Redhead, M.: Incompleteness, Nonlocality, and Realism, 2nd edn. Clarendon Press, Oxford (1989) Google Scholar
  5. 5.
    Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic, Dordrecht (1993) MATHGoogle Scholar
  6. 6.
    Werner, R.F.: Phys. Rev. A 40, 4277 (1989) CrossRefADSGoogle Scholar
  7. 7.
    Dür, W., Cirac, J.I., Tarrach, R.: Phys. Rev. Lett. 83, 3562 (1999) CrossRefADSGoogle Scholar
  8. 8.
    Dür, W., Cirac, J.I.: Phys. Rev. A 61, 042314 (2000) CrossRefMathSciNetADSGoogle Scholar
  9. 9.
    Kraus, B., Cirac, J.I., Karnas, S., Lewenstein, M.: Phys. Rev. A 61, 062302 (2000) CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Karnas, S., Lewenstein, M.: Phys. Rev. A 64, 042313 (2001) CrossRefMathSciNetADSGoogle Scholar
  11. 11.
    Fei, S.-M., Gao, X.-H., Wang, X.-H., Wang, Z.-X., Wu, K.: Phys. Rev. A 68, 022315 (2003) CrossRefADSGoogle Scholar
  12. 12.
    Doherty, A.C., Parrilo, P.A., Spedalieri, F.M.: Phys. Rev. A 69, 022308 (2004) CrossRefADSGoogle Scholar
  13. 13.
    Yu, C.-S., Song, H.-S.: Phys. Rev. A 72, 022333 (2005) CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    Chen, L., Chen, Y.-X.: Phys. Rev. A 73, 052310 (2006) CrossRefADSGoogle Scholar
  15. 15.
    Peres, A.: Phys. Rev. Lett. 77, 1413 (1996) MATHCrossRefMathSciNetADSGoogle Scholar
  16. 16.
    Horodecki, M., Horodecki, P., Horodecki, R.: Phys. Lett. A 223, 1 (1996) MATHCrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Horodecki, M., Horodecki, P., Horodecki, R.: Phys. Rev. Lett. 80, 5239 (1998) MATHCrossRefMathSciNetADSGoogle Scholar
  18. 18.
    Tóth, G., Gühne, O.: Phys. Rev. A 72, 022340 (2005) CrossRefADSGoogle Scholar
  19. 19.
    Greenberger, D.M., Horne, M.A., Zeilinger, A.: In: Kafatos, M. (ed.) Bell’s Theorem, Quantum Theory and Conceptions of the Universe, pp. 69–72. Kluwer Academic, Dordrecht (1989) Google Scholar
  20. 20.
    Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Am. J. Phys. 58, 1131 (1990) CrossRefMathSciNetADSGoogle Scholar
  21. 21.
    Benatti, F., Floreanini, R., Piani, M.: Open Syst. Inf. Dyn. 11, 325–338 (2004). arXiv:quant-ph/0411095 MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Obihiro University of Agriculture and Veterinary MedicineObihiroJapan

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