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Undetermined states: how to find them and their applications

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Abstract.

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.

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References

  1. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, e-print arXiv:quant-ph/0702225

  2. N. Linden, S. Popescu, W.K. Wootters, Phys. Rev. Lett. 89, 207901 (2002)

    Article  ADS  Google Scholar 

  3. L. Diósi, Phys. Rev. A 70, 010302 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  4. N. Linden, W.K. Wootters, Phys. Rev. Lett. 89, 277906 (2002)

    Article  ADS  Google Scholar 

  5. S.N. Walck, D.W. Lyons, Phys. Rev. Lett. 100, 050501 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  6. S.N. Walck, D.W. Lyons, Phys. Rev. A 79, 032326 (2009)

    Article  ADS  Google Scholar 

  7. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

  8. D. Gottesman, Stabilizer codes and quantum error correction, Ph.D. thesis, California Institute of Technology (1997)

  9. R. Laflamme, C. Miquel, J.P. Paz, W.H. Zurek, Phys. Rev. Lett. 77, 198 (1996)

    Article  ADS  Google Scholar 

  10. D. Gottesman, Phys. Rev. A 61, 042311 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  11. A.M. Steane, Phys. Rev. Lett. 77, 793 (1996)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. M.-Y. Ye, X.-M. Lin, Phys. Lett. A 372, 4157 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, H.-J. Briegel, e-print arXiv:quant-ph/0602096

  14. H.-K. Lo, H.F. Chau, Phys. Rev. Lett. 78, 3410 (1997)

    Article  ADS  Google Scholar 

  15. M. Hillery, V. Bužek, A. Berthiaume, Phys. Rev. A 59, 1829 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  16. S.-J. Qin, F. Gao, Q.-Y. Wen, F.-C. Zhu, Phys. Rev. A 76, 062324 (2007)

    Article  ADS  Google Scholar 

  17. D. Markham, B.C. Sanders, Phys. Rev. A 78, 042309 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  18. L.-Y. Hsu, W.-T. Yen, Chin. J. Phys. 48, 138 (2010)

    MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3, Hongo, Bunkyo-ku, Tokyo, Japan

    M. H. Hsieh

  2. Department of Physics, Chung Yuan Christian University, 32023, Chungli, Taiwan

    W. T. Yen & L. Y. Hsu

Authors
  1. M. H. Hsieh
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  2. W. T. Yen
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  3. L. Y. Hsu
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Corresponding author

Correspondence to L. Y. Hsu.

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Hsieh, M., Yen, W. & Hsu, L. Undetermined states: how to find them and their applications. Eur. Phys. J. D 61, 261–265 (2011). https://doi.org/10.1140/epjd/e2010-10374-9

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  • DOI: https://doi.org/10.1140/epjd/e2010-10374-9

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