A formal correspondence between Bayesian inference problems and the Heisenberg representation

Quantum Physics arXiv:2608.16941 (quant-ph) [Submitted on 11 Aug 2026] Title:A formal correspondence between Bayesian inference problems and the Heisenberg representation Authors:C.

Abugattas Chacoff View a PDF of the paper titled A formal correspondence between Bayesian inference problems and the Heisenberg representation, by C.

Abugattas Chacoff View PDF HTML (experimental) Abstract:The proposed formulation establishes a formal correspondence between the Heisenberg representation and the Bayesian formulation of inverse problems by identifying the observational noise operator with the initial observable. The initial observable is linked to the quadratic likelihood norm in Hilbert space, which depends on noisy observations and a direct model parameterized by unknown parameters. Using the Karhunen-Loeve expansion, the quantum state is expressed in terms of the eigenvalues and eigenfunctions of the Matern covariance. The likelihood probability is then expressed in terms of the observed state, and the model-dependent state, and is rewritten as a quadratic norm in terms of the quantum states, where the observational noise covariance is proposed to be identified with the initial observable. The main results are summarized by four theorems: the unitarity of the evolution operator, the self-adjointness of the Hamiltonian, the time invariance of the observable, and the equivalence between Heisenberg evolution and Bayesian posterior probability. Limiting cases of the Matern covariance are analyzed as the length parameter tends to zero and infinity. Finally, numerical results support the analytical findings. Subjects: Quantum Physics (quant-ph); Data Analysis, Statistics and Probability (physics.data-an) Cite as: arXiv:2608.16941 [quant-ph] (or arXiv:2608.16941v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.16941 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Carolina Abugattas [view email] [v1] Tue, 11 Aug 2026 23:22:23 UTC (684 KB) Full-text links: Access Paper: View a PDF of the paper titled A formal correspondence between Bayesian inference problems and the Heisenberg representation, by C. Abugattas ChacoffView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: physics physics.data-an 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?)