Advertisement

International Journal of Theoretical Physics

, Volume 53, Issue 3, pp 952–958 | Cite as

Note on the Wigner-Yanase-Dyson Skew Information

  • Yan-Ni Dou
  • Hong-Ke Du
Article

Abstract

In this note, releasing the restriction on operators which are observables (self-adjoint), a generalization of the Wigner-Yanase-Dyson skew information is given. We study some properties of the generalization of the Wigner-Yanase-Dyson skew information and related quantities from the operator theory point of view. In particular, an elementary proof of the convexity with the Wigner-Yanase-Dyson skew information is obtained.

Keywords

Wigner-Yanase-Dyson skew information Convexity Commutator Density operator 

Notes

Acknowledgements

The author would like to thank the anonymous referees for his/her valuable comments and suggestions which helped to improve the presentation of this paper.

References

  1. 1.
    Halmos, P.R.: A Hilbert Space Problem Book. Von Nostrand, New York (1967) MATHGoogle Scholar
  2. 2.
    Gudder, S.: Int. J. Pure Appl. Math. 39, 511 (2007) MATHMathSciNetGoogle Scholar
  3. 3.
    Wigner, E.P., Yanase, M.M.: Proc. Natl. Acad. Sci. USA (1963). doi: 10.1073/pnas.49.6.910 Google Scholar
  4. 4.
    Wang, Y.Q., Du, H.K.: J. Math. Anal. Appl. 342, 747 (2008) CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Busch, P., Heinonen, T., Lahti, P.: Phys. Rep. 452, 155 (2007) ADSCrossRefGoogle Scholar
  6. 6.
    Furuichi, S.: Phys. Rev. A 82, 034101 (2010) ADSCrossRefGoogle Scholar
  7. 7.
    Furuichi, S., Yanagi, K.: J. Math. Anal. Appl. 388, 1147 (2012) CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Gao, M.Z.: J. Math. Anal. Appl. 234, 727 (1999) CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Gibilisco, P., Isola, T.: J. Math. Anal. Appl. 375, 270 (2011) CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Heisenberg, W.: Z. Phys. A 43, 172 (1927) MATHGoogle Scholar
  11. 11.
    Li, D., Li, X., Wang, F., Huang, H., Li, X., Kwek, L.C.: arXiv:0902.3729v1 [quant-ph] 21 Feb 2009
  12. 12.
    Lieb, E.H.: Adv. Math. 11, 267 (1973) CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Luo, S.L.: Phys. Rev. A 72, 042110 (2005) ADSCrossRefGoogle Scholar
  14. 14.
    Luo, S.L., Zhang, Z.M.: J. Stat. Phys. 114, 1557 (2004) ADSCrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Robertson, H.P.: Phys. Rev. 35, 163 (1929) ADSCrossRefGoogle Scholar
  16. 16.
    Robertson, H.P.: Phys. Rev. 34, 667 (1930) Google Scholar
  17. 17.
    Schrödinger, E.: Proc. Prussian Acad. Sci., Phys. Math. XIX, 293 (1930) Google Scholar
  18. 18.
    Streater, R.F.: arXiv:math-ph/0002049v1, 27 Feb 2000
  19. 19.
    Yanagi, K.: J. Math. Anal. Appl. 380, 888 (2011) CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Yanagi, K.: J. Math. Anal. Appl. 365, 12 (2010) CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Long, G.L.: Commun. Theor. Phys. 45, 825 (2006) ADSCrossRefGoogle Scholar
  22. 22.
    Guo, Z.H., Cao, H.X.: Chin. Sci. Bull. 57, 4346 (2012) CrossRefGoogle Scholar
  23. 23.
    Guo, Z.H., Cao, H.X., Chen, Z.L., Yin, J.C.: Chin. Sci. Bull. 56, 1671 (2011) CrossRefGoogle Scholar
  24. 24.
    Long, G.L., Liu, Y.: Front. Comput. Sci. China 2, 167 (2008) CrossRefMathSciNetGoogle Scholar
  25. 25.
    Long, G.L.: Quantum Inf. Process. 6, 49 (2007) CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    Gudder, S.: Quantum Inf. Process. 6, 37 (2007) CrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    Long, G.L.: Int. J. Theor. Phys. 50, 1305 (2011) CrossRefMATHGoogle Scholar
  28. 28.
    Li, C.Y., Wang, W.Y., Wang, C., Song, S.Y.: AIP Conf. Proc. 1327, 158 (2011) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceShaanxi Normal UniversityXi’anPeople’s Republic of China

Personalised recommendations