Universal Limits on Quantum Correlations

Quantum Physics arXiv:2510.24950 (quant-ph) [Submitted on 28 Oct 2025] Title:Universal Limits on Quantum Correlations Authors:Samuel Alperin View a PDF of the paper titled Universal Limits on Quantum Correlations, by Samuel Alperin View PDF HTML (experimental) Abstract:The fundamental limits of quantum correlations set the foundation of quantum mechanics and quantum information science. Exact bounds-the Cramer-Rao inequality, the Heisenberg limit, and the Lieb-Robinson bound-have anchored entire fields, yet each applies only to a narrow class of systems or observables. Here we introduce a general framework from which all known correlation limits, as well as new ones, can be derived from a single geometric principle: the positivity of quantum state space. This intrinsic positive geometry defines a unique determinant-ratio invariant, denoted chi, which quantifies the combinatorial structure of correlations in any quantum system. Every measure of nonclassical correlation is bounded by a simple function of chi, yielding universal, model-independent floors and ceilings valid for arbitrary architectures. For systems with Lie-group symmetries, the bounds acquire compact closed forms. We recover the Heisenberg and Cramer-Rao limits and uncover previously unknown constraints, including an exact entanglement floor in multimode squeezing networks and a universal Fisher-information ceiling in fully connected spin ensembles-demonstrating that even all-to-all connectivity cannot exceed the positivity-imposed light cone in state space. Finally, we show that every correlation bound, old or new, exhibits local catastrophe-theoretic structure, with universal critical exponents classifying its approach to saturation. Positivity geometry thus provides a unified, first-principles theory of quantum limits. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2510.24950 [quant-ph] (or arXiv:2510.24950v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.24950 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Samuel Alperin [view email] [v1] Tue, 28 Oct 2025 20:33:38 UTC (19 KB) Full-text links: Access Paper: View a PDF of the paper titled Universal Limits on Quantum Correlations, by Samuel AlperinView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: math math-ph math.MP 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?)