Critical behaviors of magic and participation entropy at measurement induced phase transitions
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Quantum Physics arXiv:2603.12626 (quant-ph) [Submitted on 13 Mar 2026] Title:Critical behaviors of magic and participation entropy at measurement induced phase transitions Authors:Eliot Heinrich, Hanchen Liu, Tianci Zhou, Xiao Chen View a PDF of the paper titled Critical behaviors of magic and participation entropy at measurement induced phase transitions, by Eliot Heinrich and 3 other authors View PDF Abstract:We study the participation and stabilizer entropy of non-unitary quantum circuit dynamics, focusing on the critical line that separates the low-entanglement spin-glass phase and the paramagnetic phase. Along this critical line, the entanglement has a logarithmic scaling, which enables us to access the critical regime using large-scale matrix product state simulations with modest bond dimension. We find that both the participation entropy and stabilizer entropy exhibit critical slowing down: their saturation time scales linearly with the system size, in stark contrast to purely unitary dynamics, where saturation occurs on logarithmic time scales. In addition, we study bipartite participation and stabilizer mutual information, and find that it shows similar scaling behavior to the entanglement entropy. Finally, by analyzing the participation entropy of several paradigmatic Clifford circuits, we identify similar slow dynamical behavior near their respective critical points. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2603.12626 [quant-ph] (or arXiv:2603.12626v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.12626 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Eliot Heinrich [view email] [v1] Fri, 13 Mar 2026 03:58:53 UTC (1,817 KB) Full-text links: Access Paper: View a PDF of the paper titled Critical behaviors of magic and participation entropy at measurement induced phase transitions, by Eliot Heinrich and 3 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)