Quantum $f$-divergences via Nussbaum-Szkoła Distributions in Semifinite von Neumann Algebras

Fuente: arXiv
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Autori principali: Anastasiadis, Theodoros, Androulakis, George
Natura: Preprint
Pubblicazione: 2026
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author Anastasiadis, Theodoros
Androulakis, George
author_facet Anastasiadis, Theodoros
Androulakis, George
contents 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-Szkoła 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 $\mathbb{B}(\mathscr{H})$.
format Preprint
id arxiv_https___arxiv_org_abs_2604_19853
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Quantum $f$-divergences via Nussbaum-Szkoła Distributions in Semifinite von Neumann Algebras
Anastasiadis, Theodoros
Androulakis, George
Quantum Physics
Mathematical Physics
Operator Algebras
81P17, 46L10, 46N50
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-Szkoła 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 $\mathbb{B}(\mathscr{H})$.
title Quantum $f$-divergences via Nussbaum-Szkoła Distributions in Semifinite von Neumann Algebras
topic Quantum Physics
Mathematical Physics
Operator Algebras
81P17, 46L10, 46N50
url https://arxiv.org/abs/2604.19853