Page Curve for Local-Operator Entanglement from Free Probability
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Quantum Physics arXiv:2605.02995 (quant-ph) [Submitted on 4 May 2026] Title:Page Curve for Local-Operator Entanglement from Free Probability Authors:Neil Dowling, Silvia Pappalardi View a PDF of the paper titled Page Curve for Local-Operator Entanglement from Free Probability, by Neil Dowling and Silvia Pappalardi View PDF HTML (experimental) Abstract:The local-operator entanglement (LOE) measures the classical simulability of a Heisenberg operator and is conjectured to witness many-body chaos in locally interacting systems. Using tools from free probability, we analytically compute its value for Haar random dynamics for all Rényi indices. We find that it asymptotically reproduces the Page curve for random states in the case of traceless operators, with exponentially deviating corrections. In contrast to higher-order out-of-time ordered correlators, which depend on operator correlations via free cumulants, the leading-order LOE is independent of the initial operator. Guided by our Haar result, we therefore argue that the long-time value of the LOE entropies in chaotic systems will depend only on autocorrelation functions of the initial operator up to exponentially small corrections, suggesting that the higher-order structure of the full Eigenstate Thermalization Hypothesis is not necessary to describe it. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD) Cite as: arXiv:2605.02995 [quant-ph] (or arXiv:2605.02995v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.02995 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Neil Dowling [view email] [v1] Mon, 4 May 2026 18:00:00 UTC (123 KB) Full-text links: Access Paper: View a PDF of the paper titled Page Curve for Local-Operator Entanglement from Free Probability, by Neil Dowling and Silvia PappalardiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cond-mat cond-mat.stat-mech math math-ph math.MP nlin nlin.CD 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?)