[2301.05687] Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2301.05687 (quant-ph) [Submitted on 13 Jan 2023 ( v1 ), last revised 1 May 2026 (this version, v2)] Title: Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions Authors: Yimu Bao , Ruihua Fan , Ashvin Vishwanath , Ehud Altman View a PDF of the paper titled Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions, by Yimu Bao and 3 other authors View PDF HTML (experimental) Abstract: We develop an effective field theory characterizing the impact of decoherence on states with abelian topological order and on their capacity to protect quantum information. The decoherence appears as a temporal defect in the double topological quantum field theory that describes the pure density matrix of the uncorrupted state, and it drives a boundary phase transition involving anyon condensation at a critical coupling strength. The ensuing decoherence-induced phases and the loss of quantum information are classified by the Lagrangian subgroups of the double topological order. Our framework generalizes the error recovery transitions, previously derived for certain stabilizer codes, to generic topologically ordered states and shows that they stem from phase transitions in the intrinsic topological order characterizing the mixed state. Comments: 9 + 13 pages, 1 + 1 figures, 1 + 0 table Subjects: Quantum Physics (quant-ph) ; Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2301.05687 [quant-ph] (or arXiv:2301.05687v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2301.05687 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. Lett. 136, 220402 (2026) Related DOI : https://doi.org/10.1103/6f98-tvb8 Focus to learn more DOI(s) linking to related resources Submission history From: Yimu Bao [ view email ] [v1] Fri, 13 Jan 2023 18:15:04 UTC (688 KB) [v2] Fri, 1 May 2026 07:16:30 UTC (759 KB) Full-text links: Access Paper: View a PDF of the paper titled Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions, by Yimu Bao and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2023-01 Change to browse by: cond-mat cond-mat.str-el References & Citations INSPIRE HEP NASA ADS Google 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? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from