{
  "abstract": "We propose a holographic dual of the relative entropy of entanglement for a boundary tripartition $A:B:C$. Our proposal is that, at the leading order, \\begin{align} E_R(ρ_{AB}) = \\frac{1}{4G_N}\\Big[\\mathrm{Area}(Γ_{\\min}) - \\mathrm{Area}(γ_{AB})\\Big] \\notag \\end{align} where $Γ_{\\min}$ is the minimal bulk tripartition surface and $γ_{AB}$ is the minimal surface homologous to $AB$. For a general random tensor network, we prove the corresponding upper bound by constructing a separable state associated with $Γ_{\\min}$ and evaluating its relative entropy. We also establish the matching lower bound rigorously for networks of one, two, and three Haar random tensors by bounding the maximal tripartite product-state overlap. In appropriate geometries, the minimal tripartition surface can form a nontrivial tri-junction resembling the Mercedes logo. The proof proceeds by sequential optimization over candidate product states, which has a natural geometric interpretation as a local search for the minimal tripartition surface.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38815",
  "author_total": 2,
  "authors": [
    {
      "name": "Takato Mori"
    },
    {
      "name": "Beni Yoshida"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9367j682jqks8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38815",
  "fulltext_url": null,
  "id": "9367j682jqks8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38815",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7215047257",
  "pdf_url": "https://arxiv.org/pdf/2609.38815",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9367j682jqks8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38815",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38815"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "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": "Relative entropy of entanglement and tripartite minimal surface",
  "title_text": "Relative entropy of entanglement and tripartite minimal surface",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/9367j682jqks8",
  "venue": "arXiv",
  "versions": []
}