{
  "abstract": "Rényi multi-entropy extends the Rényi entropy to pure states of more than two parties. It is defined by a replica contraction at integer replica number $n$, and the multi-entropy is its $n\\to1$ limit. In holography this limit is conjectured to compute the area of a minimal soap-film web in the bulk. Understanding multi-entropy for general states, however, is harder. Unlike the bipartite case, the replica contraction is not a moment of a density matrix, and the continuation to $n=1$ has to be found by other means. We study this problem for qubit graph states. We show that at every odd $n$ the contraction equals $2^{-k/2}$, where $k$ is a sum of ranks of matrices over a finite field, one row and one column per qubit. We define a class of graphs that we call collision-controlled, for which the rank sum is a polynomial in $n$. This class includes graphs without even cycles and all complete bipartite graphs. The natural polynomial $n \\to 1$ continuation is a finite sum over partitions of the parties. While the Rényi multi-entropy is non-increasing under single-qubit Pauli measurements at every odd integer $n>1$, the continuation to $n=1$ is not. A $Z$ measurement on one qubit of an odd ring with $2r + 1 \\geq 7$ qubits raises it from $(r+1)\\log 2$ to $(2r-1) \\log 2$. Thus the continuation is not an entanglement monotone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27080",
  "author_total": 2,
  "authors": [
    {
      "name": "Sriram Akella"
    },
    {
      "name": "Abhijit Gadde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3r6rknk5xwt73.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27080",
  "fulltext_url": null,
  "id": "3r6rknk5xwt73",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27080",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7223153216",
  "pdf_url": "https://arxiv.org/pdf/2610.27080",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3r6rknk5xwt73.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27080",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27080"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Rényi multi-entropy of graph states and the $n -> 1$ limit",
  "title_text": "Rényi multi-entropy of graph states and the n −> 1 limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/3r6rknk5xwt73",
  "venue": "arXiv",
  "versions": []
}