{
  "abstract": "The sample complexity of identifying an unknown pure stabilizer state has been a longstanding problem in quantum information. In this paper, we resolve the entire exact critical crossover for the uniform ensemble of pure $n$-qubit stabilizer states under arbitrary collective measurements and without side information. For $k=n+c$, with fixed integer $c$, the optimal success probability converges to an explicit positive series $P_{\\infty}(c)$. In particular, $P_{\\infty}(0)=0.1760837896\\ldots$, while its two tails obey a quadratic-exponential law below threshold and $1-P_{\\infty}(c)\\sim2^{-c}$ above threshold. The pretty-good measurement is exactly optimal for every finite $n$ and $k$. The proof diagonalizes the stabilizer Gram operator through Clifford tensor-power duality and a defect filtration, including the exceptional binary sectors. The resulting integer-scale law quantifies the $n+O(1)$ copy threshold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00266",
  "author_total": 2,
  "authors": [
    {
      "name": "Masahito Hayashi"
    },
    {
      "name": "Yimin Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2dwnb8c2zp2wv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00266",
  "fulltext_url": null,
  "id": "2dwnb8c2zp2wv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00266",
  "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": "W7216465073",
  "pdf_url": "https://arxiv.org/pdf/2610.00266",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2dwnb8c2zp2wv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00266",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00266"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact Critical Curve for Uniform Stabilizer-State Identification",
  "title_text": "Exact Critical Curve for Uniform Stabilizer-State Identification",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/2dwnb8c2zp2wv",
  "venue": "arXiv",
  "versions": []
}