Monotonic multi-state quantum $f$-divergences

• URL: http://arxiv.org/abs/2103.09893v5
• Date: Tue, 26 Apr 2022 13:15:40 GMT
• Title: Monotonic multi-state quantum $f$-divergences
• Authors: Keiichiro Furuya, Nima Lashkari, Shoy Ouseph
• Abstract summary: We write down a class of multi-state quantum $f$-divergences and prove that they satisfy the data processing inequality. For two states, this class includes the $(alpha,z)$-R'enyi divergences, the $f$-divergences of Petz, and the measures in citematsumoto2015new as special cases. We conjecture that these multi-state R'enyi divergences have operational interpretations in terms of the optimal error probabilities in asymmetric multi-state quantum state discrimination.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We use the Tomita-Takesaki modular theory and the Kubo-Ando operator mean to write down a large class of multi-state quantum $f$-divergences and prove that they satisfy the data processing inequality. For two states, this class includes the $(\alpha,z)$-R\'enyi divergences, the $f$-divergences of Petz, and the measures in \cite{matsumoto2015new} as special cases. The method used is the interpolation theory of non-commutative $L^p_\omega$ spaces and the result applies to general von Neumann algebras including the local algebra of quantum field theory. We conjecture that these multi-state R\'enyi divergences have operational interpretations in terms of the optimal error probabilities in asymmetric multi-state quantum state discrimination.

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