{
  "abstract": "Estimating statistical properties of probability distributions is a fundamental problem in statistics and theoretical computer science. We develop quantum algorithms for estimating the $q$-Tsallis entropy $\\mathrm{H}_q^{\\mathrm{Tsa}}(P) =\\frac{\\sum_{i=1}^n p_i^q-1}{1-q}$ when $0<q<1$, given purified quantum query access to a distribution $P$ on $[n]$. When $0<q\\leq \\frac{1}{2}$, we provide a quantum algorithm with query complexity $\\widetilde{O}\\rbra{\\left(\\frac{n}{\\varepsilon}\\right)^{\\frac{1}{2q}}}$, which is optimal up to polylogarithmic factors. When $\\frac{1}{2}<q<1$, we introduce a two-stage simultaneous probability estimation procedure, yielding a quantum algorithm with query complexity $\\widetilde{O}\\left(\\frac{n^{\\frac12+\\frac{1}{2q}}}{\\varepsilon^{\\frac{1}{2q}}}+\\frac{n^{1-q}}{\\varepsilon}\\right)$, which improves the result given by Chen et al. (ICALP 2026) when $\\varepsilon=O\\rbra{n^{1-2q}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22983",
  "author_total": 3,
  "authors": [
    {
      "name": "Chengshen Gao"
    },
    {
      "name": "Zongxing Xiong"
    },
    {
      "name": "Lvzhou Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7eznkvscs64a8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22983",
  "fulltext_url": null,
  "id": "7eznkvscs64a8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22983",
  "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",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7222963299",
  "pdf_url": "https://arxiv.org/pdf/2610.22983",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7eznkvscs64a8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.22983",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22983"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Tsallis Entropy Estimation: Near-Optimal Bounds and High-Precision Improvements",
  "title_text": "Quantum Tsallis Entropy Estimation: Near-Optimal Bounds and High-Precision Improvements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/7eznkvscs64a8",
  "venue": "arXiv",
  "versions": []
}