{
  "abstract": "We study multi-armed bandits whose arms supply unknown quantum states and whose mean rewards are defined by a known effect $F$. Each fresh copy may be measured by an arbitrary, adaptively chosen POVM. We prove an exact collapse: the measured relative entropy from an arm state to its confusing reward half-space equals the classical Burnetas-Katehakis functional of $F$'s spectral statistics, and the spectral measurement of $F$ together with an explicit least-favorable state, built from the derivative of the matrix logarithm, forms a saddle point of the underlying measurement game. Consequently, spectral measurement followed by classical KL-UCB is asymptotically instance-optimal among all consistent single-copy policies, in every finite dimension and for every reward effect under the stated nondegeneracy assumptions: adaptive and randomized measurement design cannot improve the leading logarithmic regret coefficient, and neither can storing copies for later single-copy measurement. A self-contained finite-time bound covers general effects and boundary distributions. Any further improvement must come from measurements outside the single-copy class. For consistent policies with arbitrary quantum memory, an amortized relative-entropy argument gives a converse with the Umegaki half-space divergence, and the two per-arm regret floors, $1/K_{\\mathrm{inf}}$ and $1/D_{\\mathrm{inf}}$, coincide if and only if the arm commutes with $F$. Whether the Umegaki floor is attainable involves a composite quantum Stein problem and a separate reduction to adaptive regret; we pose it as an open problem, with two-copy numerical evidence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40339",
  "author_total": 1,
  "authors": [
    {
      "name": "Siu Hin Ng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6f1c6massfv73.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40339",
  "fulltext_url": null,
  "id": "6f1c6massfv73",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40339",
  "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",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7215126928",
  "pdf_url": "https://arxiv.org/pdf/2609.40339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6f1c6massfv73.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40339"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Single-Copy Quantum Bandit Is Classical: An Exact Spectral Collapse",
  "title_text": "The Single-Copy Quantum Bandit Is Classical: An Exact Spectral Collapse",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/6f1c6massfv73",
  "venue": "arXiv",
  "versions": []
}