Leggett-Garg Inequality Violations Bound Quantum Fisher Information
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Quantum Physics arXiv:2604.09772 (quant-ph) [Submitted on 10 Apr 2026] Title:Leggett-Garg Inequality Violations Bound Quantum Fisher Information Authors:Nick Abboud, Yuntao Guan, Barry Bradlyn, Jorge Noronha View a PDF of the paper titled Leggett-Garg Inequality Violations Bound Quantum Fisher Information, by Nick Abboud and 3 other authors View PDF HTML (experimental) Abstract:We prove that a violation of a Leggett-Garg inequality for bounded observables in stationary pure states and thermal states yields a rigorous lower bound on the quantum Fisher information. This turns a qualitative foundations test of realism in quantum systems into a quantitative witness of useful quantum sensitivity and, in the collective setting, into a lower bound on multipartite entanglement depth in many-body systems. We further demonstrate that Leggett-Garg violations are constrained by the same spectral moments, susceptibilities, and $f$-sum-rule bounds that organize many-body response. Our results show that temporal correlations of a single collective observable can serve as an experimentally accessible witness of many-body quantum coherence, without requiring full state reconstruction. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th) Cite as: arXiv:2604.09772 [quant-ph] (or arXiv:2604.09772v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.09772 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nick Abboud [view email] [v1] Fri, 10 Apr 2026 18:00:34 UTC (124 KB) Full-text links: Access Paper: View a PDF of the paper titled Leggett-Garg Inequality Violations Bound Quantum Fisher Information, by Nick Abboud and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cond-mat cond-mat.stat-mech hep-th 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?)