Stability of Maximum-Entropy Inference in Finite Dimensions

Quantum Physics arXiv:2510.21095 (quant-ph) [Submitted on 24 Oct 2025] Title:Stability of Maximum-Entropy Inference in Finite Dimensions Authors:James Tian View a PDF of the paper titled Stability of Maximum-Entropy Inference in Finite Dimensions, by James Tian View PDF HTML (experimental) Abstract:We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The maximum-entropy principle selects the Gibbs state that agrees with the data while remaining maximally unbiased. We prove that convergence of moments and entropy implies convergence of states in trace norm, derive explicit quantitative bounds linking data and entropy deviations to state distance, and show that these results are stable under unital completely positive maps. The analysis is self-contained and relies on convex duality, relative entropy, and Pinsker-type inequalities, providing a rigorous and unified foundation for finite-dimensional maximum-entropy inference. Subjects: Quantum Physics (quant-ph); Functional Analysis (math.FA) MSC classes: Primary: 94A17, secondary: 47N50, 81P45 Cite as: arXiv:2510.21095 [quant-ph] (or arXiv:2510.21095v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.21095 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: James Tian [view email] [v1] Fri, 24 Oct 2025 02:13:48 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled Stability of Maximum-Entropy Inference in Finite Dimensions, by James TianView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: math math.FA 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)