{
  "abstract": "We study the action of quantum channels on states on a von Neumann algebra $\\mathcal{M}$ with conserved quantities encoded by a subalgebra $\\mathcal{N}$. We define a phase as an equivalence class of normal states on $\\mathcal{M}$ under the action of quantum channels preserving $\\mathcal{N}$. First, we establish a relative quasi-entropic characterization of phase equivalence using the Petz recovery map. We further introduce the operator algebra (OA) symmetry of a state and define an equivalence relation between OA symmetries via bishifts of biprojections. When $\\mathcal{N}\\subseteq\\mathcal{M}$ is an irreducible finite-index subfactor of type II$_1$, we prove that phase equivalence implies OA symmetry equivalence. Consequently, OA symmetry breaking provides a sufficient mechanism for detecting phase transitions. Furthermore, combining finite-index subfactor theory with quantum Fourier analysis, we prove that the cardinality of each phase is finite and obtain an explicit upper bound depending only on the Jones index.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20879",
  "author_total": 4,
  "authors": [
    {
      "name": "Linzhe Huang"
    },
    {
      "name": "Chunlan Jiang"
    },
    {
      "name": "Zhengwei Liu"
    },
    {
      "name": "Jinsong Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jgqzt9w2vsyh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20879",
  "fulltext_url": null,
  "id": "8jgqzt9w2vsyh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20879",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213904239",
  "pdf_url": "https://arxiv.org/pdf/2609.20879",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8jgqzt9w2vsyh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2609.20879",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20879"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Equivalence of states and bimodule quantum channels",
  "title_text": "Equivalence of states and bimodule quantum channels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/8jgqzt9w2vsyh",
  "venue": "arXiv",
  "versions": []
}