{
  "abstract": "We study the query complexity of testing quantum juntas. Given an unknown $n$-qubit unitary or quantum channel, the goal is to decide whether it acts nontrivially on at most $k$ qubits or is $\\varepsilon$-far from every such operation. For unitaries, we consider the forward-only model, where the tester has access to $U$, but not to $U^\\dagger$ or controlled-$U$. We give tight bounds for both unitary and channel junta testing. For sufficiently large $k$, $n \\ge 2k$, and a broad range of $\\varepsilon$, both problems have query complexity $Θ\\left(k/(\\varepsilon^2\\log k)\\right)$. Our upper bounds are achieved by simple nonadaptive testers using product inputs and single-qubit measurements. For junta channels, this closes the gap by Bao and Yao (COLT 23, TPAMI 2025) between an $\\widetilde{O}(k)$ upper bound and a $\\widetildeΩ(\\sqrt{k})$ lower bound at constant $\\varepsilon$, establishing the optimal $Θ(k/\\log k)$ query complexity. At the heart of both bounds is a strong connection between quantum junta testing and classical support-size testing. For the upper bounds, we reduce quantum junta testing to a generalized support-size problem for distributions over random subsets, and develop a new tester with improved sample complexity. For the lower bounds, we proceed in the reverse direction, reducing classical support-size testing to quantum junta testing through a phase-masked hard ensemble and showing that forward quantum queries can be exactly classicalized on average. Together, these reductions identify support-size testing as the classical core of quantum junta testing and yield matching lower bounds. At constant $\\varepsilon$, they also give a separation between $Θ(k/\\log k)$ forward queries and $\\widetilde{O}(\\sqrt{k})$ queries with inverse access.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37926",
  "author_total": 3,
  "authors": [
    {
      "name": "Jinge Bao"
    },
    {
      "name": "Minbo Gao"
    },
    {
      "name": "Penghui Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6byjw8jv44fc4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37926",
  "fulltext_url": null,
  "id": "6byjw8jv44fc4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37926",
  "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": "W7214900886",
  "pdf_url": "https://arxiv.org/pdf/2609.37926",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6byjw8jv44fc4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37926",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37926"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal Quantum Junta Testing without Inverse Queries",
  "title_text": "Optimal Quantum Junta Testing without Inverse Queries",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:36Z",
  "url": "https://research.draconitic.com/paper/6byjw8jv44fc4",
  "venue": "arXiv",
  "versions": []
}