{
  "abstract": "Coherent noise can give rise to unconventional regimes of quantum information recovery and mixed-state order. We study these phenomena in two settings related by Wegner duality: the triangular-lattice surface code subject to single-qubit Pauli-$Z$ rotations followed by syndrome measurements, and a $\\mathbb{Z}_2$ paramagnet subject to strongly symmetric decoherence. Increasing the rotation angle drives a transition from a decodable phase to a \\emph{partially decodable} critical phase in the code, and from a strongly symmetric phase to a phase with \\emph{algebraic} $\\mathbb{Z}_2$ strong-to-weak spontaneous symmetry breaking (SWSSB) in the dual paramagnet. We develop a common description of these phenomena in terms of a weakly coupled $\\mathrm{SO}(n)$ nonlinear sigma model in the replica limit $n\\to1$. Taking this replica limit analytically, we derive universal signatures of the critical phase: an optimal Pauli decoding fidelity that approaches a universal function of the system's aspect ratio in the thermodynamic limit, and a dual fidelity correlator that decays as a universal power law. These observables relate to correlations of twist operators in the sigma model description. Large-scale numerical simulations confirm these analytical predictions. We also argue that the algebraic SWSSB phase cannot be realized by any Pauli dephasing channel acting on the $\\mathbb{Z}_{2}$ paramagnet. We probe this \"non-classical\" character through the output state's sensitivity to well-separated $\\mathbb{Z}_{2}$ fluxes inserted in the initial state, which reveals persistent coherence between distinct $\\mathbb{Z}_{2}$ charge trajectories at long distances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40567",
  "author_total": 3,
  "authors": [
    {
      "name": "Stephen W. Yan"
    },
    {
      "name": "Yimu Bao"
    },
    {
      "name": "Sagar Vijay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ejcven2ewad7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40567",
  "fulltext_url": null,
  "id": "4ejcven2ewad7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40567",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ejcven2ewad7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40567"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Algebraic strong-to-weak symmetry breaking and partial decodability in the surface code",
  "title_text": "Algebraic strong-to-weak symmetry breaking and partial decodability in the surface code",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/4ejcven2ewad7",
  "venue": "arXiv",
  "versions": []
}