{
  "abstract": "We show that nonadaptive single-qubit Pauli measurements suffice to test whether an unknown $n$-qubit state $ρ$ is $\\varepsilon$-close to or $O(\\varepsilon)$-far from an ideal target state $|ψ\\rangle$, for all but a $2^{-Ω(n)}$ fraction of target states. The test uses $O(\\varepsilon^{-2}\\log(1/δ))$ copies of $ρ$ to achieve confidence $1-δ$, which is information-theoretically optimal even among protocols with arbitrary joint measurements. The main technical innovation is an uncertainty principle for weighted generalizations of the total influence of Boolean functions. As a simple example, the unweighted variant states that $\\mathbf{Inf}[f]+\\mathbf{Inf}[\\widehat{f}] = Ω(n)$, which is a natural hypercube analogue of the Heisenberg uncertainty principle (here $\\widehat{\\,\\cdot\\,}$ denotes the $2^{-n/2}$-normalized Fourier transform). The weighted case generalizes $\\mathbf{Inf}[\\,\\cdot\\,]$ and $\\mathbf{Inf}[\\,\\widehat{\\,\\cdot\\,}\\,]$ to Dirichlet energies associated with Glauber dynamics for certain dual measures on the cube.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.27184",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrea Coladangelo"
    },
    {
      "name": "Jerry Li"
    },
    {
      "name": "Joseph Slote"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27qpcftzcfa4m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.27184",
  "fulltext_url": null,
  "id": "27qpcftzcfa4m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.27184",
  "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": "W7171828215",
  "pdf_url": "https://arxiv.org/pdf/2607.27184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27qpcftzcfa4m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2607.27184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.27184"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Robust quantum state certification and uncertainty principles for total influence",
  "title_text": "Robust quantum state certification and uncertainty principles for total influence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/27qpcftzcfa4m",
  "venue": "arXiv",
  "versions": []
}