Quantum Cram\'{e}r-Rao bound on quantum metric as a multi-observable uncertainty relation
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Quantum Physics arXiv:2603.04615 (quant-ph) [Submitted on 4 Mar 2026] Title:Quantum Cramér-Rao bound on quantum metric as a multi-observable uncertainty relation Authors:Wei Chen View a PDF of the paper titled Quantum Cram\'{e}r-Rao bound on quantum metric as a multi-observable uncertainty relation, by Wei Chen View PDF HTML (experimental) Abstract:A version of quantum Cramér-Rao bound dictates that the covariance of any set of operators is bounded by a product of the derivatives of expectation values and the inverse of quantum metric. We elaborate that because quantum metric itself is the covariance of the generators of translation in the parameter space, quantum metric in any dimension is bounded by a product of itself and Berry curvature. The generator formalism further indicates that the bound is equivalent to a multi-observable uncertainty relation, which in the two-operator case recovers the Robertson-Schrödinger uncertainty relation. The momentum space quantum metric and spin operators of three-dimensional topological insulators under magnetic field are used to demonstrate the validity of the three-operator version of these bounds. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.04615 [quant-ph] (or arXiv:2603.04615v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.04615 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Wei Chen [view email] [v1] Wed, 4 Mar 2026 21:20:09 UTC (93 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Cram\'{e}r-Rao bound on quantum metric as a multi-observable uncertainty relation, by Wei ChenView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)