Stability of mixed-state phases under weak decoherence

Quantum Physics arXiv:2511.01976 (quant-ph) [Submitted on 3 Nov 2025] Title:Stability of mixed-state phases under weak decoherence Authors:Yifan F. Zhang, Sarang Gopalakrishnan View a PDF of the paper titled Stability of mixed-state phases under weak decoherence, by Yifan F. Zhang and 1 other authors View PDF HTML (experimental) Abstract:We prove that the Gibbs states of classical, and commuting-Pauli, Hamiltonians are stable under weak local decoherence: i.e., we show that the effect of the decoherence can be locally reversed. In particular, our conclusions apply to finite-temperature equilibrium critical points and ordered low-temperature phases. In these systems the unconditional spatio-temporal correlations are long-range, and local (e.g., Metropolis) dynamics exhibits critical slowing down. Nevertheless, our results imply the existence of local "decoders" that undo the decoherence, when the decoherence strength is below a critical value. An implication of these results is that thermally stable quantum memories have a threshold against decoherence that remains nonzero as one approaches the critical temperature. Analogously, in diffusion models, stability of data distributions implies the existence of computationally-efficent local denoisers in the late-time generation dynamics. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); Mathematical Physics (math-ph) Cite as: arXiv:2511.01976 [quant-ph] (or arXiv:2511.01976v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.01976 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yifan Zhang [view email] [v1] Mon, 3 Nov 2025 19:00:02 UTC (1,370 KB) Full-text links: Access Paper: View a PDF of the paper titled Stability of mixed-state phases under weak decoherence, by Yifan F. Zhang and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: cond-mat cond-mat.stat-mech cs cs.LG math math-ph math.MP 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?)