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

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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.

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Authors and Affiliations

  1. Department of Physics and NTZ, Karl-Marx-University, DDR-701, Leipzig, German Democratic Republic

    A. Uhlmann

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  1. A. Uhlmann
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Communicated by H. Araki

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Uhlmann, A. Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory. Commun.Math. Phys. 54, 21–32 (1977). https://doi.org/10.1007/BF01609834

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  • DOI: https://doi.org/10.1007/BF01609834

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