{
  "abstract": "Non-invertible symmetries extend conventional symmetries beyond group-like transformations and play an important role in quantum field theory and many-body physics. However, a general framework of non-invertible symmetries in open quantum systems is still lacking. Here, we formulate a general Liouville-space duality framework that extends Hilbert-space non-invertible dualities to open quantum systems. The resulting defect relates Liouvillians with dual Hamiltonian and dissipative parameters and becomes an exact symmetry at self-duality. We apply this framework to the periodic transverse-field Ising chain with two collective Lindblad channels exchanged by Kramers--Wannier (KW) duality. A strong $\\mathbb{Z}_2$ symmetry divides Liouville space into four parity sectors, while the defect acts nontrivially only in the even-even sector. At self-duality, the KW defect imposes a momentum-resolved selection rule on Liouvillian Jordan blocks. Modes with different Liouville momenta or KW-defect eigenvalues cannot form a common exceptional Jordan block. For a three-site chain, a global Rényi-2 KW asymmetry dynamically identifies the self-dual conditions. At the same time, the spectral structure exhibits both a semisimple degeneracy and a self-dual exceptional point with a perturbation-selective response. These results extend non-invertible dualities to Markovian quantum dynamics and establish a symmetry-based selection rule for Liouvillian Jordan structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23111",
  "author_total": 3,
  "authors": [
    {
      "name": "Ying-Cheng Yang"
    },
    {
      "name": "Jhen-Dong Lin"
    },
    {
      "name": "Yueh-Nan Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61mwxfgpyv13d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23111",
  "fulltext_url": null,
  "id": "61mwxfgpyv13d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23111",
  "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.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7222931501",
  "pdf_url": "https://arxiv.org/pdf/2610.23111",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61mwxfgpyv13d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.23111",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23111"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Liouvillian Non-Invertible Symmetry",
  "title_text": "Liouvillian Non-Invertible Symmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/61mwxfgpyv13d",
  "venue": "arXiv",
  "versions": []
}