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Quantum f-Divergences in von Neumann Algebras

Part of the book series: Mathematical Physics Studies ((MPST))

Abstract

The notion of quantum divergences has played a significant role in quantum information, which defines important quantum quantities to discriminate between states of a quantum system. A quantum system is mathematically described, in most cases, by an operator algebra \(\mathcal {A}\) on a Hilbert space, either finite-dimensional or infinite-dimensional, and a quantum divergence is generally given as a function S(ψ∥φ) of two states or more generally, two positive linear functionals ψ and φ on \(\mathcal {A}\). This monograph is aimed at presenting a comprehensive survey of quantum f-divergences and showing their significant role in the reversibility problem of quantum operations in the general von Neumann algebra setting.

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Authors and Affiliations

  1. Abiko, Chiba, Japan

    Fumio Hiai

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  1. Fumio Hiai
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Hiai, F. (2021). Introduction. In: Quantum f-Divergences in von Neumann Algebras. Mathematical Physics Studies. Springer, Singapore. https://doi.org/10.1007/978-981-33-4199-9_1

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