{
  "abstract": "Pure-state quantum phases are defined through finite-depth local unitary connections. This concept of phases has recently been generalized to mixed states in terms of locally reversible channels. In this work, we establish a fundamental relation between mixed-state phases and pure-state phases. We show that a locally reversible channel between mixed states can be lifted to a local isometry between their canonical purifications; thus, if two mixed states are in the same phase, then their canonical purifications are in the same pure-state phase. Furthermore, an explicit construction of the lifting isometry is given by ``half'' of the Petz recovery map, suggesting that the Petz recovery map \\emph{without rotation} is enough to connect mixed state phases. We illustrate our results with two examples: toric code under bit flip noise and Chern insulator under fermion number noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41926",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiaoyang Huang"
    },
    {
      "name": "Shengqi Sang"
    },
    {
      "name": "Chong Wang"
    },
    {
      "name": "Yijian Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zvmnx27a8fp9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41926",
  "fulltext_url": null,
  "id": "9zvmnx27a8fp9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41926",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41926",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zvmnx27a8fp9.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.41926",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41926"
    }
  ],
  "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": "Lifting the mixed to the pure: quantum phases of matter from canonical purification",
  "title_text": "Lifting the mixed to the pure: quantum phases of matter from canonical purification",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/9zvmnx27a8fp9",
  "venue": "arXiv",
  "versions": []
}