{
  "abstract": "We study genuine multi-entropy as a diagnostic of multipartite entanglement in the toric code, which provides a controlled setting for probing multipartite structures in topologically ordered states. Our main question is whether genuine multi-entropy captures information that is not reducible to conventional lower-party entropic data, such as topological entanglement entropy. We first analyze toric-code ground states that admit a stabilizer-state description, where the relevant quantities can be evaluated exactly. We conjecture that, for stabilizer states and $\\mathtt{q}\\ge4$, the $\\mathtt{q}$-partite genuine multi-entropy at replica index $n<\\mathtt{q}$ collapses to a linear combination of multi-entropies involving at most $\\mathtt{q}-2$ parties. We establish this pattern explicitly for $\\mathtt{q}=4$ in the toric code stabilizer sector: for $n=2,3$, the genuine multi-entropy is proportional to the tripartite information $I_3$ and, for the Kitaev-Preskill partition, contains no independent genuine four-partite information beyond that captured by the topological entanglement entropy. At $n=4$, however, this reduction breaks down: the genuine multi-entropy is no longer proportional to $I_3$, but remains a topological invariant of the toric-code stabilizer ground states under Kitaev-Preskill-preserving deformations that do not change whether the numbers of vertex- and plaquette-type junctions coincide. For generic non-stabilizer superpositions within the ground-state manifold and for coherent superpositions of local excitations, the low-$n$ reduction also fails. These results show that genuine multi-entropy probes multipartite entanglement structure beyond the tripartite information, and hence beyond the topological entanglement entropy in the Kitaev-Preskill partition, whereas for stabilizer states at low replica index it reduces to lower-partite entropic data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.06050",
  "author_total": 3,
  "authors": [
    {
      "name": "Sriram Akella"
    },
    {
      "name": "Norihiro Iizuka"
    },
    {
      "name": "Akihiro Miyata"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/88yj8t6r7jc2e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.06050",
  "fulltext_url": null,
  "id": "88yj8t6r7jc2e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.06050",
  "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": "W7167669372",
  "pdf_url": "https://arxiv.org/pdf/2607.06050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/88yj8t6r7jc2e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2607.06050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.06050"
    }
  ],
  "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": "Genuine Multi-Entropy in the Toric Code",
  "title_text": "Genuine Multi-Entropy in the Toric Code",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/88yj8t6r7jc2e",
  "venue": "arXiv",
  "versions": []
}