Freeness Reined in by a Single Qubit

Quantum Physics arXiv:2512.13803 (quant-ph) [Submitted on 15 Dec 2025] Title:Freeness Reined in by a Single Qubit Authors:Alexander Altland, Francisco Divi, Tobias Micklitz, Maedeh Rezaei View a PDF of the paper titled Freeness Reined in by a Single Qubit, by Alexander Altland and 3 other authors View PDF HTML (experimental) Abstract:Free probability provides a framework for describing correlations between non-commuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework under a minimal deviation from freeness: the coupling of a single ancilla qubit to a Haar-distributed quantum circuit of dimension $D0 \gg 1$. We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$. These modifications persist at long times, when the dynamics of the coupled system is already ergodic. We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn) Cite as: arXiv:2512.13803 [quant-ph] (or arXiv:2512.13803v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.13803 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Maedeh Rezaei [view email] [v1] Mon, 15 Dec 2025 19:00:09 UTC (469 KB) Full-text links: Access Paper: View a PDF of the paper titled Freeness Reined in by a Single Qubit, by Alexander Altland and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cond-mat cond-mat.dis-nn 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?)