Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory View Full Text


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Article Info

DATE

1977-02

AUTHORS

A. Uhlmann

ABSTRACT

We show that the Wigner-Yanase-Dyson-Lieb concavity is a general property of an interpolation theory which works between pairs of (hilbertian) seminorms. As an application, the theory extends the relevant work of Lieb and Araki to positive linear forms of arbitrary *-algebras. In this context a “relative entropy” is defined for every pair of positive linear forms of a *-algebra with identity. For this generalized relative entropy its joint convexity and its decreasing under identity-preserving completely positive maps is proved. More... »

PAGES

21-32

References to SciGraph publications

  • 1936-12. Über konvexe Matrixfunktionen in MATHEMATISCHE ZEITSCHRIFT
  • 1974-06. Expectations and entropy inequalities for finite quantum systems in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01609834

    DOI

    http://dx.doi.org/10.1007/bf01609834

    DIMENSIONS

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