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

  • X. Li
  • D. LiEmail author
  • H. Huang
  • X. Li
  • L. C. Kwek
Regular Article Quantum Information


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.


Entropy Mixed State Pure State Generalize Entropy Unitary Transformation 
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  1. 1.
    A. Wehrl, Rev. Mod. Phys. 50, 221 (1978)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948)MathSciNetzbMATHGoogle Scholar
  3. 3.
    M.A. Nielsen, I.C. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000), p. 89Google Scholar
  4. 4.
    A.I. Khinchin, Mathematical Foundations of Information Theory (Dover Publication, New York, 1957)Google Scholar
  5. 5.
    C. Tsallis S. LIoyd, M. Baranger, Phys. Rev. A 63, 042104 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    R. Renner, N. Gisin, B. Kraus, Phys. Rev. A 72, 012332 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    V. Giovannetti, S. Lloyd, Phys. Rev. A 69, 062307 (2004)MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    I. Bialynicki-Birula, Phys. Rev. A 74, 052101 (2006)MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    G. Wilk, Z. Wlodarczyk, Phys. Rev. Lett. 84, 2770 (2000)ADSCrossRefGoogle Scholar
  10. 10.
    G. Wilk, Z. Wlodarczyk, Phys. Rev. D 43, 794 (1991)ADSCrossRefGoogle Scholar
  11. 11.
    J. Batle, M. Casas, A.R. Plastino, A. Plastino, Phys. Lett. A 296, 251 (2002)MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. 12.
    X. Hu, Z. Ye, J. Math. Phys. 47, 023502 (2006)MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    S. Luo, Phys. Rev. A 73, 022324 (2006)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    C. Brukner, A. Zeilinger, Phys. Rev. A 63, 022113 (2001)ADSCrossRefGoogle Scholar
  15. 15.
    E.P. Wigner, M.M. Yanase, Proc. Natl. Acad. Sci. USA 49, 910 (1963)MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    S. Luo, Phys. Rev. A 72, 042110 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    S. Luo, Phys. Rev. Lett. 91, 180403 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    S. Luo, Theor. Math. Phys. 143, 681 (2005)zbMATHCrossRefGoogle Scholar
  19. 19.
    Z.Q. Chen, Phys. Rev. A 71, 052302 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    F. Hansen, J. Statist. Phys. 126, 643 (2007)ADSzbMATHCrossRefGoogle Scholar
  21. 21.
    P. Gibilisco, T. Isola, Inf. Dimen. Anal. Quan. Prob. Rel. Top. 11, 127 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    E.H. Lieb, Adv. Math. 11, 267 (1973)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    D. Li, X. Li, F. Wang, H. Huang, X. Li, L.C. Kwek, Phys. Rev. A 79, 052106 (2009)MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    M. Hirvensalo, Quantum computing (Springer-Verlag, Berlin, 2001)Google Scholar
  25. 25.
    S. Abe, Phys. Rev. A 65, 052323 (2002)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.Department of mathematical sciencesTsinghua UniversityBeijingP.R. China
  3. 3.Electrical Engineering and Computer Science DepartmentUniversity of MichiganAnn ArborUSA
  4. 4.Department of Computer ScienceWayne State UniversityDetroitUSA
  5. 5.National Institute of EducationNanyang Technological UniversitySingaporeSingapore
  6. 6.Center for Quantum TechnologiesNational Univeristy of SingaporeSingaporeSingapore
  7. 7.Institute of Advanced StudiesNanyang Technological UniversitySingaporeSingapore

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