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

• URL: http://arxiv.org/abs/2604.19853v1
• Date: Tue, 21 Apr 2026 15:41:37 GMT
• Title: Quantum $f$-divergences via Nussbaum-Szkoła Distributions in Semifinite von Neumann Algebras
• Abstract summary: We prove that the quantum $f$-divergence between two normal states on a semifinite vonNeumann algebra is equal to the classical $f$-divergence between two corresponding classical states.<n>We extend their result for normal states on any semifinite vonNeumann algebra, not only $mathbbB(mathscrH)$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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-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 $\mathbb{B}(\mathscr{H})$.

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