Skip to main content
SpringerLink
Log in

Expectations and entropy inequalities for finite quantum systems

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We prove that the relative entropy is decreasing under a trace-preserving expectation inB(K 1), and we show the connection between this theorem and the strong subadditivity of the entropy. It is also proved that a linear, positive, trace-preserving map Φ ofB(K) into itself such that ‖Φ‖≦1 decreases the value of any convex trace function.

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. Lieb, E. H., Ruskai, M. B.: J. Math. Phys.14, 1938–1941 (1973)

    Google Scholar 

  2. Umegaki, H.: Kodai Math. Sem. Rep.14, 59–85 (1962)

    Google Scholar 

  3. Kullback, S.: Information theory and statistics. New York: Wiley 1959

    Google Scholar 

  4. Lieb, E. H.: Adv. Math.11, 267–288 (1973)

    Google Scholar 

  5. Lindblad, G.: Commun. math. Phys.33, 305–322 (1973)

    Google Scholar 

  6. Tomiyama, J.: Proc. Japan Acad.33, 608–612 (1957)

    Google Scholar 

  7. Arveson, W. B.: Am. J. Math.89, 578–672 (1967)

    Google Scholar 

  8. Kovács, I., Szücs, J.: Acta Math. Sci., Szeged,27, 233–246 (1966)

    Google Scholar 

  9. Schwartz, J. T.:W*-algebras. New York: Gordon and Breach 1967

    Google Scholar 

  10. Lindblad, G.: Commun. math. Phys.28, 245–249 (1972)

    Google Scholar 

  11. Nakamura, M., Umegaki, H.: Proc. Japan Acad.37, 149–154 (1961)

    Google Scholar 

  12. Segal, I. E.: J. Math. Mech.9, 623–629 (1960)

    Google Scholar 

  13. Ruelle, D.: Statistical mechanics. New York: Benjamin 1969

    Google Scholar 

  14. Baumann, F.: Helv. Phys. Acta44, 95–100 (1971)

    Google Scholar 

  15. Bendat, J., Sherman, S.: Trans. Am. Math. Soc.79, 58–71 (1955)

    Google Scholar 

  16. Stinespring, W. F.: Proc. Am. Math. Soc.6, 211–216 (1955)

    Google Scholar 

  17. Davis, C.: Proc. Am. Math. Soc.8, 41–44 (1957)

    Google Scholar 

  18. Nakamura, M., Takesaki, M., Umegaki, H.: Kodai Math. Sem. Rep.12, 82–90 (1960)

    Google Scholar 

  19. Gohberg, I. C., Krein, M. G.: Introduction to the theory of linear non-selfadjoint operators. Providence: Am. Math. Soc. 1969

  20. Hardy, G. H., Littlewood, J. E., Polya, G.: Inequalities. Cambridge: University Press 1934

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Physics, Royal Institute of Technology, Stockholm, Sweden

    Göran Lindblad

Authors
  1. Göran Lindblad
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by H. Araki

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lindblad, G. Expectations and entropy inequalities for finite quantum systems. Commun.Math. Phys. 39, 111–119 (1974). https://doi.org/10.1007/BF01608390

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01608390

Keywords

Search

Navigation