{
  "abstract": "The entanglement structure of a bipartite pure state is characterized by its entanglement spectrum, or equivalently, by the family of Rényi-$k$ entanglement entropies with integer $k$. Taking the difference of two such entropies defines a quantity known as an entanglement spread, that is monotonous under local operations, and that vanishes if and only if the entanglement spectrum of the state is flat. We introduce a multipartite generalization of this notion which, for a fixed number $D\\geq 3$ of parties, results in a collection of maps indexed by pairs of $D$-edge-colored graphs (obeying some condition). Each member of this collection takes the form of a difference of two multipartite Rényi entanglement entropies, each associated to a local unitary polynomial invariant (known in this context as a trace-invariant), and is shown to be monotonous under local operations. We then argue that a previously introduced family of so-called hypergraph-tensor (HT) states can be understood as a multipartite counterpart to the family of flat bipartite states. Indeed, we first prove that, when $D=3$, a tripartite pure state is HT if and only if it minimizes a particular (infinite) family of entanglement spreads. Second, we embed the set of HT states into the much larger family of spectral hypergraph-tensor (SHT) states, defined by a new Ansatz we introduce. We then prove that HT states can be uniquely characterized as the minimizers of some fixed entanglement spread among SHT states, for arbitrary $D\\geq 3$. We also investigate SHT states in their own right: in particular, we characterize their orbits under local unitary transformations. Finally, along the way, the asymptotic large-$N$ expectation values of a number of entanglement spreads are computed in the Haar-random state of local dimension $N$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12271",
  "author_total": 3,
  "authors": [
    {
      "name": "Sylvain Carrozza"
    },
    {
      "name": "Johann Chevrier"
    },
    {
      "name": "Luca Lionni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/009ys8byabkaw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12271",
  "fulltext_url": null,
  "id": "009ys8byabkaw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12271",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7221114560",
  "pdf_url": "https://arxiv.org/pdf/2610.12271",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/009ys8byabkaw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.12271",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12271"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Multipartite entanglement spreads",
  "title_text": "Multipartite entanglement spreads",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/009ys8byabkaw",
  "venue": "arXiv",
  "versions": []
}