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A variational expression for the relative entropy

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Abstract

We prove that for the relative entropy of faithful normal states ϕ and ω on the von Neumann algebraM the formula

$$S(\varphi ,\omega ) = \sup \{ \omega (h) - \log \varphi ^h (I):h = h^* \in M\}$$

holds.

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Authors and Affiliations

  1. Mathematical Institute of HAS, Reàltanoda u. 13–15, PF.127, H-1364, Budapest, Hungary

    Dénes Petz

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  1. Dénes Petz
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Communicated by H. Araki

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Petz, D. A variational expression for the relative entropy. Commun.Math. Phys. 114, 345–349 (1988). https://doi.org/10.1007/BF01225040

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