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International Conference on Geometric Science of Information

GSI 2021: Geometric Science of Information pp 154–162Cite as

Quantum Jensen-Shannon Divergences Between Infinite-Dimensional Positive Definite Operators

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12829))

Abstract

This work studies a parametrized family of symmetric divergences on the set of Hermitian positive definite matrices which are defined using the \(\alpha \)-Tsallis entropy \(\forall \alpha \in \mathbb {R}\). This family unifies in particular the Quantum Jensen-Shannon divergence, defined using the von Neumann entropy, and the Jensen-Bregman Log-Det divergence. The divergences, along with their metric properties, are then generalized to the setting of positive definite trace class operators on an infinite-dimensional Hilbert space \(\forall \alpha \in \mathbb {R}\). In the setting of reproducing kernel Hilbert space (RKHS) covariance operators, all divergences admit closed form formulas in terms of the corresponding kernel Gram matrices.

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Author information

Authors and Affiliations

  1. RIKEN Center for Advanced Intelligence Project, Tokyo, Japan

    Hà Quang Minh

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  1. Hà Quang Minh
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Correspondence to Hà Quang Minh .

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Editors and Affiliations

  1. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

  2. THALES Land & Air Systems, Meudon, France

    Frédéric Barbaresco

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Minh, H.Q. (2021). Quantum Jensen-Shannon Divergences Between Infinite-Dimensional Positive Definite Operators. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_18

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  • DOI: https://doi.org/10.1007/978-3-030-80209-7_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-80208-0

  • Online ISBN: 978-3-030-80209-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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