{
  "abstract": "We study how large the certificate complexity ${C}(f)$ of a total Boolean function can be relative to its randomized and quantum query complexities. We construct a total Boolean function $f$ whose randomized query complexity with one-sided error satisfies ${R}_1(f) = Θ(\\sqrt{{C}(f)})$. This separation is optimal even when two-sided error is allowed. From this construction, we obtain another total Boolean function $F$ with bounded-error quantum query complexity ${Q}(F) = \\widetilde O({C}(F)^{1/4})$, attaining the general quartic bound up to polylogarithmic factors. For the same function, both exact and zero-error quantum query complexities are $\\widetilde O(\\sqrt{{C}(F)})$. We also prove matching lower bounds for these two measures on $F$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11664",
  "author_total": 3,
  "authors": [
    {
      "name": "Andris Ambainis"
    },
    {
      "name": "Jānis Iraids"
    },
    {
      "name": "Martins Kokainis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82z71dzjebgxy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11664",
  "fulltext_url": null,
  "id": "82z71dzjebgxy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11664",
  "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": "W7212277564",
  "pdf_url": "https://arxiv.org/pdf/2609.11664",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82z71dzjebgxy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.11664",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11664"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Near-Optimal Separations of Certificate Complexity from Randomized and Quantum Query Complexity",
  "title_text": "Near-Optimal Separations of Certificate Complexity from Randomized and Quantum Query Complexity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/82z71dzjebgxy",
  "venue": "arXiv",
  "versions": []
}