{
  "abstract": "The three-tangle, $τ_3$, is a measure of genuine tripartite entanglement that distinguishes GHZ-type from W-type entanglement in pure three-qubit states. Here, we identify the statistically optimal one-sided four-copy detector of the three-tangle and study its implementation cost. The optimal detector has click probability $τ_3^2/48$, while previous four-copy constructions achieve $τ_3^2/256$ and therefore require asymptotically $16/3$ times as many experimental repetitions. Using the representation-theoretic structure of the problem, we construct an ancilla-free implementation of the optimal detector using 15 CNOT gates, together with an 11-CNOT detector with click probability $τ_3^2/96$. These results reveal a tradeoff between statistical efficiency and implementation cost, since reducing the number of repetitions requires increasingly expensive circuits. We then show that this tradeoff persists once the circuits are encoded. In a fully fault-tolerant setting, the increased click probability comes with a substantial non-Clifford synthesis cost, while an early fault-tolerant implementation based on $T$ gates and STAR rotations reduces this overhead at the expense of additional encoded resources. We quantify these costs using both the Steane and $[[8,3,2]]$ codes, providing explicit resource estimates for implementing the optimal detector across different computational regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27260",
  "author_total": 6,
  "authors": [
    {
      "name": "Federico Tomás B. Pérez"
    },
    {
      "name": "Berta Casas"
    },
    {
      "name": "I-Chi Chen"
    },
    {
      "name": "Su Yeon Chang"
    },
    {
      "name": "Philipp Schleich"
    },
    {
      "name": "M. Cerezo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ae26nrezpm3y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27260",
  "fulltext_url": null,
  "id": "3ae26nrezpm3y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27260",
  "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",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7223143160",
  "pdf_url": "https://arxiv.org/pdf/2610.27260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ae26nrezpm3y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27260"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal four-copy detection of the three-tangle and its fault-tolerant cost",
  "title_text": "Optimal four-copy detection of the three-tangle and its fault-tolerant cost",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/3ae26nrezpm3y",
  "venue": "arXiv",
  "versions": []
}