{
  "abstract": "Entangling rates describe a direct entangling channel, but give no information when that channel is forbidden. For finite-dimensional analytic pure-state dynamics, we show that the onset of genuine $(n+1)$-partite entanglement is determined by the contact order $m_\\star$ between the physical trajectory and the $S|E$ product manifold. It is the first Taylor order that cannot be reproduced by any product curve, or equivalently the first nonvanishing order of the Fubini--Study distance from the product manifold. We derive a time-ordered recursion that removes curvature-induced kinematic terms and computes $m_\\star$ from the Taylor coefficients of $H(t)$. This provides a geometric description of an entanglement cascade, in which new subsystems can join multipartite entanglement only after one or more interaction steps. A symmetry-protected three-qubit model realizes $m_\\star=2$, and a three-mode bosonic example shows that genuine tripartite entanglement can arise even when the two newly formed reduced pairs remain separable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06675",
  "author_total": 2,
  "authors": [
    {
      "name": "Sugumi Kanno"
    },
    {
      "name": "Jiro Soda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fm3xrdh8ckgbx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06675",
  "fulltext_url": null,
  "id": "fm3xrdh8ckgbx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06675",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7211998062",
  "pdf_url": "https://arxiv.org/pdf/2609.06675",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fm3xrdh8ckgbx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.06675",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06675"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Contact order governs the onset of entanglement cascades",
  "title_text": "Contact order governs the onset of entanglement cascades",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/fm3xrdh8ckgbx",
  "venue": "arXiv",
  "versions": []
}