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arXiv · 2604.19853

Quantum $f$-divergences via Nussbaum-Szko{\l}a Distributions in Semifinite von Neumann Algebras

Theodoros Anastasiadis·George Androulakis
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Abstract

In this article, we prove that the quantum $f$-divergence between two normal states on a semifinite von~Neumann algebra is equal to the classical $f$-divergence between two corresponding classical states, which are called Nussbaum-Szko{\l}a distributions. This result has been proved by the second named author and T.C.~John for normal states on the von~Neumann algebra $\mathbb{B}(\mathscr{H})$ of all bounded operators on a Hilbert space $\mathscr{H}$. We extend their result for normal states on any semifinite von~Neumann algebra, not only $\mathbb{B}(\mathscr{H})$.

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BibTeXRIS

Theodoros Anastasiadis, George Androulakis. 2026-04-21. Quantum $f$-divergences via Nussbaum-Szko{\l}a Distributions in Semifinite von Neumann Algebras. https://arxiv.org/abs/2604.19853

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