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

Quantum Physics [Submitted on 21 Apr 2026] Quantum f-divergences via Nussbaum-Szkoła Distributions in Semifinite von Neumann Algebras Theodoros Anastasiadis, George Androulakis 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}). Comments: 30 pages Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Operator Algebras (math.OA) MSC classes: 81P17, 46L10, 46N50 Cite as: arXiv:2604.19853 [quant-ph]   (or arXiv:2604.19853v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.19853 Focus to learn more Submission history From: Theodoros Anastasiadis [view email] [v1] Tue, 21 Apr 2026 15:41:37 UTC (24 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: math math-ph math.MP math.OA References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)