{
  "abstract": "We study quantum state tomography when the unknown state lies in a trace-distance ball of radius $R$ around a known reference state $ρ$. For arbitrary collective measurements, we determine the minimax expected risk and confidence radius up to universal constants, uniformly over the dimension, center spectrum, radius, and sample size. Write $Γ=d(\\mathrm{Tr}\\sqrtρ)^2+d^2R$. For $d\\ge2$, $0<R\\le1$, and $n\\ge1$ copies, the expected risk is $Θ(\\min\\{R,\\sqrt{Γ/n}\\})$. At failure probability $0<δ\\le1/3$, the minimax confidence radius is \\[ Θ\\!\\left(\\min\\left\\{R,\\sqrt{\\frac{Γ+\\log(1/δ)}{n}}\\right\\}\\right). \\] For $\\varepsilon\\le c_0R$ with a universal $c_0>0$, the copy complexity is $Θ((Γ+\\log(1/δ))/\\varepsilon^2)$. For the lower bound we use a weighted trace-norm witness to retain all spectral scales in a square-root perturbation family. For the upper bound, we give a direct spectral and concentration analysis of a modified existing purification-based procedure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05374",
  "author_total": 1,
  "authors": [
    {
      "name": "Yonglong Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/71xap07weeq3f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05374",
  "fulltext_url": null,
  "id": "71xap07weeq3f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05374",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7220656039",
  "pdf_url": "https://arxiv.org/pdf/2610.05374",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/71xap07weeq3f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.05374",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05374"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Minimax Quantum State Tomography in a Known Trace-Distance Ball",
  "title_text": "Minimax Quantum State Tomography in a Known Trace-Distance Ball",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/71xap07weeq3f",
  "venue": "arXiv",
  "versions": []
}