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Averaged Wigner-Yanase-Dyson information as a quantum uncertainty measure

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Abstract

The average of the skew information over the observables was proposed by Luo as a quantum uncertainty measure. In this paper, we investigate the interesting properties of Wigner-Yanase-Dyson (WYD) information, which is a generalization of skew information. Then, by averaging WYD information over the observables we propose a general quantum uncertainty measure of mixed states, and study the properties of the measure. Note that the general quantum uncertainty measure depends on the parameter α and reduces to Luo’s measure when α is equal to 1/2. To get rid of the parameter α, we propose the average of the general measure over the parameter α as a quantum uncertainty measure of mixed states and discuss its properties. The two measures can be considered as the intrinsic properties of mixed state. The construction is reminiscent of the generalized entropies that have shown to be useful in many applications.

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References

  1. A. Wehrl, Rev. Mod. Phys. 50, 221 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  2. C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948)

    MathSciNet  MATH  Google Scholar 

  3. M.A. Nielsen, I.C. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000), p. 89

  4. A.I. Khinchin, Mathematical Foundations of Information Theory (Dover Publication, New York, 1957)

  5. C. Tsallis S. LIoyd, M. Baranger, Phys. Rev. A 63, 042104 (2001)

    Article  ADS  Google Scholar 

  6. R. Renner, N. Gisin, B. Kraus, Phys. Rev. A 72, 012332 (2005)

    Article  ADS  Google Scholar 

  7. V. Giovannetti, S. Lloyd, Phys. Rev. A 69, 062307 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  8. I. Bialynicki-Birula, Phys. Rev. A 74, 052101 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  9. G. Wilk, Z. Wlodarczyk, Phys. Rev. Lett. 84, 2770 (2000)

    Article  ADS  Google Scholar 

  10. G. Wilk, Z. Wlodarczyk, Phys. Rev. D 43, 794 (1991)

    Article  ADS  Google Scholar 

  11. J. Batle, M. Casas, A.R. Plastino, A. Plastino, Phys. Lett. A 296, 251 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. X. Hu, Z. Ye, J. Math. Phys. 47, 023502 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  13. S. Luo, Phys. Rev. A 73, 022324 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  14. C. Brukner, A. Zeilinger, Phys. Rev. A 63, 022113 (2001)

    Article  ADS  Google Scholar 

  15. E.P. Wigner, M.M. Yanase, Proc. Natl. Acad. Sci. USA 49, 910 (1963)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. S. Luo, Phys. Rev. A 72, 042110 (2005)

    Article  ADS  Google Scholar 

  17. S. Luo, Phys. Rev. Lett. 91, 180403 (2003)

    Article  ADS  Google Scholar 

  18. S. Luo, Theor. Math. Phys. 143, 681 (2005)

    Article  MATH  Google Scholar 

  19. Z.Q. Chen, Phys. Rev. A 71, 052302 (2005)

    Article  ADS  Google Scholar 

  20. F. Hansen, J. Statist. Phys. 126, 643 (2007)

    Article  ADS  MATH  Google Scholar 

  21. P. Gibilisco, T. Isola, Inf. Dimen. Anal. Quan. Prob. Rel. Top. 11, 127 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  22. E.H. Lieb, Adv. Math. 11, 267 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  23. D. Li, X. Li, F. Wang, H. Huang, X. Li, L.C. Kwek, Phys. Rev. A 79, 052106 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  24. M. Hirvensalo, Quantum computing (Springer-Verlag, Berlin, 2001)

  25. S. Abe, Phys. Rev. A 65, 052323 (2002)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, CA, 92697-3875, USA

    X. Li

  2. Department of mathematical sciences, Tsinghua University, Beijing, 100084, P.R. China

    D. Li

  3. Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, MI, 48109, USA

    D. Li & H. Huang

  4. Department of Computer Science, Wayne State University, Detroit, MI, 48202, USA

    X. Li

  5. National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, 637616, Singapore, Singapore

    L. C. Kwek

  6. Center for Quantum Technologies, National Univeristy of Singapore, 3 Science Drive 2, 117543, Singapore, Singapore

    L. C. Kwek

  7. Institute of Advanced Studies, Nanyang Technological University, 60 Nanyang View, 639673, Singapore, Singapore

    L. C. Kwek

Authors
  1. X. Li
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  2. D. Li
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  3. H. Huang
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  4. X. Li
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  5. L. C. Kwek
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Correspondence to D. Li.

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Li, X., Li, D., Huang, H. et al. Averaged Wigner-Yanase-Dyson information as a quantum uncertainty measure. Eur. Phys. J. D 64, 147–153 (2011). https://doi.org/10.1140/epjd/e2011-20017-4

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  • DOI: https://doi.org/10.1140/epjd/e2011-20017-4

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