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Leggett-Garg Inequality Violations Bound Quantum Fisher Information

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arXiv:2604.09772v1 Announce Type: new 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 th

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Quantum Physics [Submitted on 10 Apr 2026] Leggett-Garg Inequality Violations Bound Quantum Fisher Information Nick Abboud, Yuntao Guan, Barry Bradlyn, Jorge Noronha 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: 13 pages, 1 figure. Includes supplemental material 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 Submission history From: Nick Abboud [view email] [v1] Fri, 10 Apr 2026 18:00:34 UTC (124 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev | next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.stat-mech hep-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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