Vanishing correlations in (bi)stochastic controlled circuits
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Quantum Physics arXiv:2601.14379 (quant-ph) [Submitted on 20 Jan 2026] Title:Vanishing correlations in (bi)stochastic controlled circuits Authors:Pavel Kos, Bruno Bertini, Tomaž Prosen View a PDF of the paper titled Vanishing correlations in (bi)stochastic controlled circuits, by Pavel Kos and 2 other authors View PDF HTML (experimental) Abstract:We study the dynamics of circuits composed of stochastic and bistochastic controlled gates. This type of dynamics arises from quantum circuits with random controlled gates, as well as in stochastic circuits and deterministic classical cellular automata. We prove that stochastic and bistochastic controlled gates lead to two-point spatio-temporal correlation functions that vanish everywhere except when the two operators act on the same site. More generally, for multi-point correlations the two rightmost operators must act on the same site. We argue that autocorrelation, while hard to compute, typically decays exponentially towards a value that is exponentially small in the system size. Our results reveal a broad class of quantum systems that exhibit surprisingly simple correlation structures despite their complex microscopic dynamics. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2601.14379 [quant-ph] (or arXiv:2601.14379v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.14379 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Pavel Kos [view email] [v1] Tue, 20 Jan 2026 19:00:05 UTC (139 KB) Full-text links: Access Paper: View a PDF of the paper titled Vanishing correlations in (bi)stochastic controlled circuits, by Pavel Kos and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cond-mat cond-mat.stat-mech 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?)