{
  "abstract": "We prove that every pure state of stabilizer rank at most $k$ has stabilizer extent at most $2^{O(\\sqrt{k\\log(k+1)})}$, and establish the analogous bound for the squared Clifford coefficient norm of Clifford-rank-$k$ operators. This implies stabilizer fidelity at least $2^{-O(\\sqrt{k\\log(k+1)})}$, resolving the quantitative conjecture of (Mehraban-Tamasbi, STOC, 2025), and proves an $Ω(n^2/\\log n)$ lower bound for the approximate stabilizer rank of tensor powers of any non-stabilizer qubit state. The latter result generalizes the best-known lower bound for tensor powers of $T$-states (Mehraban-Tamasbi, STOC, 2024) to arbitrary non-stabilizer qubit states, including magic states. As a consequence of the Clifford rank--norm inequality, we obtain an $Ω(n^2/\\log n)$ lower bound for exact representations of $n$-bit AND function by quadratic phases, improving the previous best-known linear bound. Further consequences rule out pseudorandom state and unitary ensembles with approximate stabilizer and Clifford rank $O((\\log n)^2/\\log\\log n)$, respectively, a $\\log n$ improvement over prior work (Kalra-Sinha, Quantum, 2026). We also obtain tomography algorithms for states of stabilizer rank at most $k$, with $poly(n)2^{O(\\sqrt{k\\log(k+1)})}$ time and copy complexity, a nearly square-root improvement in the exponent over the best-known algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06819",
  "author_total": 2,
  "authors": [
    {
      "name": "Pulkit Sinha"
    },
    {
      "name": "Benjamin Lovitz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/81gp1xcjz2gbn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06819",
  "fulltext_url": null,
  "id": "81gp1xcjz2gbn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06819",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220681077",
  "pdf_url": "https://arxiv.org/pdf/2610.06819",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/81gp1xcjz2gbn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:05Z",
      "native_id": "2610.06819",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06819"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Improved bounds on stabilizer extent and Clifford rank",
  "title_text": "Improved bounds on stabilizer extent and Clifford rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:05Z",
  "url": "https://research.draconitic.com/paper/81gp1xcjz2gbn",
  "venue": "arXiv",
  "versions": []
}