Variational formulae for entropy-like functionals for states in von Neumann algebras
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912638113415168 |
|---|---|
| author | Łuczak, Andrzej Podsędkowska, Hanna Wieczorek, Rafał |
| author_facet | Łuczak, Andrzej Podsędkowska, Hanna Wieczorek, Rafał |
| contents | The paper presents variational formulae for entropy-like functionals, including Segal and Rényi entropies, for normal states on semifinite von Neumann algebras. The considered functionals are of the form $τ(f(h))$ where $τ$ is a normal faithful semifinite trace on this algebra, $h$ is a positive selfadjoint operator from $L^1(\M,τ)$, and $f$ is an appropriate convex or concave function. The results cover both finite and semifinite algebras, and the obtained formulae generalise known results, in particular, those concerning relative entropy. Moreover, the connection between quantum entropies and the structure of abelian subalgebras is highlighted, providing new interpretations in the context of quantum information theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational formulae for entropy-like functionals for states in von Neumann algebras Łuczak, Andrzej Podsędkowska, Hanna Wieczorek, Rafał Operator Algebras Mathematical Physics Functional Analysis Quantum Algebra Quantum Physics The paper presents variational formulae for entropy-like functionals, including Segal and Rényi entropies, for normal states on semifinite von Neumann algebras. The considered functionals are of the form $τ(f(h))$ where $τ$ is a normal faithful semifinite trace on this algebra, $h$ is a positive selfadjoint operator from $L^1(\M,τ)$, and $f$ is an appropriate convex or concave function. The results cover both finite and semifinite algebras, and the obtained formulae generalise known results, in particular, those concerning relative entropy. Moreover, the connection between quantum entropies and the structure of abelian subalgebras is highlighted, providing new interpretations in the context of quantum information theory. |
| title | Variational formulae for entropy-like functionals for states in von Neumann algebras |
| topic | Operator Algebras Mathematical Physics Functional Analysis Quantum Algebra Quantum Physics |
| url | https://arxiv.org/abs/2510.07605 |