{
  "abstract": "We present a pure-state tomography algorithm that uses a nearly minimal number of measurement settings while achieving optimal sample complexity with nonadaptive single-copy shallow Clifford measurements. For an arbitrary $n$-qubit pure state $|ψ\\rangle \\in \\mathbb{C}^{d}$, where $d=2^n$, the algorithm uses $O(d/ε)$ copies and $\\widetilde{O}(1)$ measurement settings to output a state vector $|\\hatψ\\rangle$ satisfying $1-|\\langleψ|\\hatψ\\rangle|^2\\leε$ with high probability. Each measurement is implemented by a Clifford circuit of depth $O(\\log n)$. Reusing each measurement setting allows the data to be stored compactly as per-basis outcome histograms. Given these histograms, classical post-processing runs in $\\widetilde{O}(d)$ time. Our key technique, \\textit{shadow bootstrapping}, uses the current estimate to reduce the variance of subsequent residual estimation, enabling progressively more accurate reconstruction with only a constant number of new measurement settings per stage.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06073",
  "author_total": 2,
  "authors": [
    {
      "name": "Gyungmin Cho"
    },
    {
      "name": "Dohun Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e8y0ee8pew8mn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06073",
  "fulltext_url": null,
  "id": "e8y0ee8pew8mn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06073",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06073",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e8y0ee8pew8mn.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.06073",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06073"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Shadow bootstrapping: Nearly minimal-setting pure-state tomography with shallow Clifford measurements",
  "title_text": "Shadow bootstrapping: Nearly minimal-setting pure-state tomography with shallow Clifford measurements",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:19Z",
  "url": "https://research.draconitic.com/paper/e8y0ee8pew8mn",
  "venue": "arXiv",
  "versions": []
}