Skip to main content
SpringerLink
Log in

WYD-like Skew Information Measures

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Following recent advances in the theory of operator monotone functions we introduce new classes of WYD-like skew information measures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Araki, H., Yanase, M.M.: Measurement of quantum mechanical operators. Phys. Rev. 120, 622–626 (1960)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Bendat, J., Sherman, S.: Monotone and convex operator functions. Trans. Am. Math. Soc. 79, 58–71 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cai, L., Hansen, F.: Metric-adjusted skew information: convexity and restricted forms of superadditivity. Lett. Math. Phys. 93, 1–13 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Hansen, F.: Selfadjoint means and operator monotone functions. Math. Ann. 256, 29–35 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hansen, F.: Characterizations of symmetric monotone metrics on the state space of quantum systems. Quantum Inf. Comput. 6, 597–605 (2006)

    MathSciNet  MATH  Google Scholar 

  6. Hansen, F.: Metric adjusted skew information. Proc. Natl. Acad. Sci. USA 105, 9909–9916 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Hansen, F.: Convexity of quantum χ 2-divergence. Proc. Natl. Acad. Sci. USA 108, 10078–10080 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Hansen, F.: The fast track to Löwner’s theorem. Linear Algebra Appl. doi:10.1016/j.laa.2013.01.022 (2011). arXiv:1112.0098.

    Google Scholar 

  9. Hasegawa, H.: α-Divergence of the non-commutative information geometry. Rep. Math. Phys. 33, 87–93 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Hasegawa, H., Petz, D.: On the Riemannian metric of α-entropies of density matrices. Lett. Math. Phys. 38, 221–225 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Jencova, A., Ruskai, M.B.: A unified treatment of convexity of relative entropy and related trace functions, with conditions for equality. Rev. Math. Phys. 22(9), 1099–1121 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kawasaki, M., Nagisa, M.: Transforms on operator monotone functions. arXiv:1206.5452v1 (2012)

  13. Lieb, E.: Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math. 11, 267–288 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  14. Luo, S.: Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91, 180403 (2003)

    Article  ADS  Google Scholar 

  15. Morozova, E.A., Chentsov, N.N.: Markov invariant geometry on state manifolds. Itogi Nauki Techn. 36, 69–102 (1990) (in Russian). Translated in J. Soviet Math. 56, 2648–2669 (1991)

    Google Scholar 

  16. Petz, D.: Monotone metrics on matrix spaces. Linear Algebra Appl. 244, 81–96 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wigner, E.P.: Die Messung quantenmechanischer Operatoren. Z. Phys. 133, 101–108 (1952)

    MathSciNet  ADS  MATH  Google Scholar 

  18. Wigner, E.P., Yanase, M.M.: Information contents of distributions. Proc. Natl. Acad. Sci. USA 49, 910–918 (1963)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tohoku University, Sendai, Miyagi, Japan

    Frank Hansen

Authors
  1. Frank Hansen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Frank Hansen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hansen, F. WYD-like Skew Information Measures. J Stat Phys 151, 974–979 (2013). https://doi.org/10.1007/s10955-013-0737-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-013-0737-5

Keywords

Search

Navigation