Quantum $f$-divergences via Nussbaum-Szkoła Distributions in Semifinite von Neumann Algebras
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913053631578112 |
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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 |