Beyond Wigner: Non-Invertible Symmetries Preserve Probabilities
Summarize this article with:
Quantum Physics arXiv:2602.07110 (quant-ph) [Submitted on 6 Feb 2026] Title:Beyond Wigner: Non-Invertible Symmetries Preserve Probabilities Authors:Thomas Bartsch, Yuhan Gai, Sakura Schafer-Nameki View a PDF of the paper titled Beyond Wigner: Non-Invertible Symmetries Preserve Probabilities, by Thomas Bartsch and 2 other authors View PDF Abstract:In recent years, the traditional notion of symmetry in quantum theory was expanded to so-called generalised or categorical symmetries, which, unlike ordinary group symmetries, may be non-invertible. This appears to be at odds with Wigner's theorem, which requires quantum symmetries to be implemented by (anti)unitary -- and hence invertible -- operators in order to preserve probabilities. We resolve this puzzle for (higher) fusion category symmetries $\mathcal{C}$ by proposing that, instead of acting by unitary operators on a fixed Hilbert space, symmetry defects in $\mathcal{C}$ act as isometries between distinct Hilbert spaces constructed from twisted sectors. As a result, we find that non-invertible symmetries naturally act as trace-preserving quantum channels. Crucially, our construction relies on the symmetry category $\mathcal{C}$ being unitary. We illustrate our proposal through several examples that include Tambara-Yamagami, Fibonacci, and Yang-Lee as well as higher categorical symmetries. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA) Cite as: arXiv:2602.07110 [quant-ph] (or arXiv:2602.07110v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.07110 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sakura Schafer-Nameki [view email] [v1] Fri, 6 Feb 2026 19:00:00 UTC (488 KB) Full-text links: Access Paper: View a PDF of the paper titled Beyond Wigner: Non-Invertible Symmetries Preserve Probabilities, by Thomas Bartsch and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cond-mat cond-mat.str-el hep-ph hep-th math math.QA 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?)