{
  "abstract": "We study the following quantum state identity problem: given access to copies of $n$ unknown pure quantum states, the goal is to determine whether every pair has fidelity at least $1-\\varepsilon$ or some pair has fidelity at most $\\varepsilon$. This problem relaxes the identical-or-orthogonal promise considered in previous work. For any fixed overlap parameter $\\varepsilon\\in(0,1/4)$, we present two quantum algorithms with complementary guarantees on circuit depth and sample complexity. The first runs in constant depth using parallel swap tests and takes $O(\\log(n/δ)\\log(2/δ))$ copies of each input state to succeed with probability at least $1-δ$. The second uses the Schur transform to reduce the sample complexity to $O(\\log(n/δ))$, through an analysis relating Jucys--Murphy elements to Schur sampling. We also prove a matching sample complexity lower bound of $Ω(\\log(n/δ))$ for any quantum algorithm with failure probability at most $δ\\le 1/2-c$, for any constant $c>0$, establishing that the second algorithm achieves the optimal dependence on both $n$ and $δ$ for fixed $\\varepsilon$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04597",
  "author_total": 2,
  "authors": [
    {
      "name": "Shih-Han Hung"
    },
    {
      "name": "Ming-Hsien Tsai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ywwt4cm60jjc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04597",
  "fulltext_url": null,
  "id": "0ywwt4cm60jjc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04597",
  "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 Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220688510",
  "pdf_url": "https://arxiv.org/pdf/2610.04597",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ywwt4cm60jjc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.04597",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04597"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Efficient Quantum State Identity Testing",
  "title_text": "Efficient Quantum State Identity Testing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/0ywwt4cm60jjc",
  "venue": "arXiv",
  "versions": []
}