The European Physical Journal D

, Volume 61, Issue 1, pp 261–265 | Cite as

Undetermined states: how to find them and their applications

  • M. H. Hsieh
  • W. T. Yen
  • L. Y. HsuEmail author


We investigate the undetermined sets consisting of two-level, multi-partite pure quantum states, whose reduced density matrices give absolutely no information of their original states. Two approached of finding these quantum states are proposed. One is to establish the relation between codewords of the stabilizer quantum error correction codes (SQECCs) and the undetermined states. The other is to study the local complementation rules of the graph states. As an application, the undetermined states can be exploited in the quantum secret sharing scheme. The security is guaranteed by their undetermineness.


Logic State Graph State Quantum Cryptography Quantum Secret Sharing Reduce Density Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, e-print arXiv:quant-ph/0702225
  2. 2.
    N. Linden, S. Popescu, W.K. Wootters, Phys. Rev. Lett. 89, 207901 (2002) CrossRefADSGoogle Scholar
  3. 3.
    L. Diósi, Phys. Rev. A 70, 010302 (2004) CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    N. Linden, W.K. Wootters, Phys. Rev. Lett. 89, 277906 (2002) CrossRefADSGoogle Scholar
  5. 5.
    S.N. Walck, D.W. Lyons, Phys. Rev. Lett. 100, 050501 (2008) CrossRefMathSciNetADSGoogle Scholar
  6. 6.
    S.N. Walck, D.W. Lyons, Phys. Rev. A 79, 032326 (2009) CrossRefADSGoogle Scholar
  7. 7.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000) Google Scholar
  8. 8.
    D. Gottesman, Stabilizer codes and quantum error correction, Ph.D. thesis, California Institute of Technology (1997) Google Scholar
  9. 9.
    R. Laflamme, C. Miquel, J.P. Paz, W.H. Zurek, Phys. Rev. Lett. 77, 198 (1996) CrossRefADSGoogle Scholar
  10. 10.
    D. Gottesman, Phys. Rev. A 61, 042311 (2000) CrossRefMathSciNetADSGoogle Scholar
  11. 11.
    A.M. Steane, Phys. Rev. Lett. 77, 793 (1996) zbMATHCrossRefMathSciNetADSGoogle Scholar
  12. 12.
    M.-Y. Ye, X.-M. Lin, Phys. Lett. A 372, 4157 (2008) CrossRefMathSciNetADSzbMATHGoogle Scholar
  13. 13.
    M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, H.-J. Briegel, e-print arXiv:quant-ph/0602096
  14. 14.
    H.-K. Lo, H.F. Chau, Phys. Rev. Lett. 78, 3410 (1997) CrossRefADSGoogle Scholar
  15. 15.
    M. Hillery, V. Bužek, A. Berthiaume, Phys. Rev. A 59, 1829 (1999) CrossRefMathSciNetADSGoogle Scholar
  16. 16.
    S.-J. Qin, F. Gao, Q.-Y. Wen, F.-C. Zhu, Phys. Rev. A 76, 062324 (2007) CrossRefADSGoogle Scholar
  17. 17.
    D. Markham, B.C. Sanders, Phys. Rev. A 78, 042309 (2008) CrossRefMathSciNetADSGoogle Scholar
  18. 18.
    L.-Y. Hsu, W.-T. Yen, Chin. J. Phys. 48, 138 (2010) MathSciNetGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3, Hongo, Bunkyo-kuTokyoJapan
  2. 2.Department of PhysicsChung Yuan Christian UniversityChungliTaiwan

Personalised recommendations