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arXiv · 1805.02050

Quantum $f$-divergences in von Neumann algebras I. Standard $f$-divergences

Fumio Hiai
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Abstract

We make a systematic study of standard $f$-divergences in general von Neumann algebras. An important ingredient of our study is to extend Kosaki's variational expression of the relative entropy to an arbitary standard $f$-divergence, from which most of the important properties of standard $f$-divergences follow immediately. In a similar manner we give a comprehensive exposition on the Rényi divergence in von Neumann algebra. Some results on relative hamiltonians formerly studied by Araki and Donald are improved as a by-product.

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Fumio Hiai. 2018-05-05. Quantum $f$-divergences in von Neumann algebras I. Standard $f$-divergences. https://doi.org/10.1063/1.5039973

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