{
  "abstract": "We introduce a real-valued functional $I(\\vec{n}_1,\\vec{n}_2)$ of four three-qubit correlations that turns the Greenberger-Horne-Zeilinger (GHZ) algebraic paradox into a quantitative witness of genuine tripartite entanglement. For every three-qubit state $ρ$ and every pair of directions, $|I(\\vec{n}_1,\\vec{n}_2;ρ)|\\le 2$, with equality if and only if $\\vec{n}_1\\perp\\vec{n}_2$ and $ρ$ is locally unitarily equivalent to the GHZ state. On the five-parameter Acín family, $I(\\hat{x},\\hat{y})$ depends only on $λ_0λ_4$ and is maximised by the GHZ state; for the W state $I(\\hat{x},\\hat{y})=0$ and $\\max|I_{\\mathrm{W}}|=35/27$. Maximising over independent local orthonormal frames yields a local-unitary invariant measure $\\mathcal{E}_{\\mathrm{GHZ}}\\in[0,1]$, computable from four three-body Pauli correlators, that equals one exactly on the GHZ orbit and takes the values $35/54$ on the W state and $1/2$ on product states. We show that $\\mathcal{E}_{\\mathrm{GHZ}}$ is not convex: an equal mixture of three biseparable states has $\\mathcal{E}_{\\mathrm{GHZ}}=14/27$, larger than the average $1/2$ of its components. We also relate $\\mathcal{E}_{\\mathrm{GHZ}}$ to GHZ fidelity witnesses, discuss its behaviour under local operations and classical communication, and outline a generalisation to three qudits via Heisenberg-Weyl operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.02876",
  "author_total": 3,
  "authors": [
    {
      "name": "Shengjun Wu"
    },
    {
      "name": "Kaichen Zhong"
    },
    {
      "name": "Jeffery Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8d15h6rvy1tdy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.02876",
  "fulltext_url": null,
  "id": "8d15h6rvy1tdy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.02876",
  "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",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.02876",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8d15h6rvy1tdy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2605.02876",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.02876"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A measure for genuine tripartite entanglement",
  "title_text": "A measure for genuine tripartite entanglement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/8d15h6rvy1tdy",
  "venue": "arXiv",
  "versions": []
}