Recoverable states on von-Neumann algebras
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Quantum Physics arXiv:2605.08829 (quant-ph) [Submitted on 9 May 2026] Title:Recoverable states on von-Neumann algebras Authors:Saptak Bhattacharya View a PDF of the paper titled Recoverable states on von-Neumann algebras, by Saptak Bhattacharya View PDF HTML (experimental) Abstract:Let $(\mathcal{M},\tau)$ and $(\mathcal{N},\tau^{\prime})$ be tracial von-Neumann algebras and let $\phi:\mathcal{M}\to\mathcal{N}$ be a strictly completely positive, trace preserving map. Given a positive, invertible $B\in\mathcal{M}$ with $\tau(B)=1$, a state on $\mathcal{M}$ given by a positive $A\in L^1(\mathcal{M}, \tau)$ is said to be recoverable if $\mathcal{R}(\phi(A))=A$ where $\mathcal{R}$ is the Petz recovery map corresponding to $B$ and $\phi$. In this paper, we study recoverable states and show how an arbitrary state can be made close to a recoverable state via iterates of $\mathcal{R}\circ\phi$. We show that there exists a completely positive, trace preserving map $\psi:\mathcal{M}\to\mathcal{M}$ such that $\psi(A)$ is recoverable for all $A$ and $(\mathcal{R}\circ\phi)^n\to\psi$ in norm as operators on $L^p(\mathcal{M},\tau)$ for all $1\,\textless p\,\textless\infty$, and discuss potential applications to quantum information theory. We also show that this convergence holds strongly in $L^1$. Finally, we prove an interesting decomposition theorem for normal states on $\mathcal{M}$. Comments: Subjects: Quantum Physics (quant-ph); Functional Analysis (math.FA); Operator Algebras (math.OA) MSC classes: 81P17, 46L52 Cite as: arXiv:2605.08829 [quant-ph] (or arXiv:2605.08829v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.08829 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Saptak Bhattacharya [view email] [v1] Sat, 9 May 2026 09:33:39 UTC (10 KB) Full-text links: Access Paper: View a PDF of the paper titled Recoverable states on von-Neumann algebras, by Saptak BhattacharyaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math.FA math.OA References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)