Multiparameter function estimation for general Hamiltonians
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Quantum Physics arXiv:2605.04136 (quant-ph) [Submitted on 5 May 2026] Title:Multiparameter function estimation for general Hamiltonians Authors:Erfan Abbasgholinejad, Sean R. Muleady, Jacob Bringewatt, Lorcan O. Conlon, Alexey V. Gorshkov View a PDF of the paper titled Multiparameter function estimation for general Hamiltonians, by Erfan Abbasgholinejad and 4 other authors View PDF HTML (experimental) Abstract:Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the corresponding bound for estimating a function of multiple parameters-each coupled to distinct and possibly non-commuting generators-remains unknown in general. Here, we derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian that attains this bound. We show that, although the task is fundamentally a multiparameter problem, our tight bound reduces to an optimized single-parameter quantum Cramér-Rao bound, even for arbitrary generator sets. Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.04136 [quant-ph] (or arXiv:2605.04136v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.04136 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Erfan Abbasgholinejad [view email] [v1] Tue, 5 May 2026 18:00:00 UTC (35 KB) Full-text links: Access Paper: View a PDF of the paper titled Multiparameter function estimation for general Hamiltonians, by Erfan Abbasgholinejad and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)