{
  "abstract": "Entropy estimation of discrete probability distributions is a fundamental problem in statistical inference and quantum property estimation. In this paper, we study the problem of estimating Rényi entropy $H_α(\\mathbf{p})$ for any distribution $\\mathbf{p} = (p_i)_{i=1}^n$ given its purified quantum query-access. For non-integer $α> 1$, our algorithm estimates $H_α(\\mathbf{p})$ to within additive error $ε$ using only $\\widetilde{\\mathcal{O}}\\big(n^{\\max\\{1/2,1-1/α\\}}/ε\\big)$ queries, which improves the best known upper bound for dependence on both $n$ and $1/ε$. For $0<α<1$, our algorithm has query complexity $\\widetilde{\\mathcal{O}}\\big(n^{1/(2α)}/ε^{\\max\\{1,1/(2α)\\}}\\big)$, which improves the dependence on $1/ε$ of the current best upper bound without incresing its $n$ dependence. Our approach adapts the multi-level estimation framework to relative approximation of the power sums and leverage binary search to remove the requirement of prior knowledge of them. We also strengthen the precision-dependent lower bound to $Ω\\big(1/ε^{\\max\\{1,1/(2α)\\}}\\big)$ for $0<α<1$, which identifies the optimal precision dependence of our algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19936",
  "author_total": 3,
  "authors": [
    {
      "name": "Zongxing Xiong"
    },
    {
      "name": "Chengshen Gao"
    },
    {
      "name": "Lvzhou Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f70k3m91er2qs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19936",
  "fulltext_url": null,
  "id": "f70k3m91er2qs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19936",
  "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": "W7222185347",
  "pdf_url": "https://arxiv.org/pdf/2610.19936",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f70k3m91er2qs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.19936",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19936"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Improved Quantum Algorithms for Rényi Entropies Estimation",
  "title_text": "Improved Quantum Algorithms for Rényi Entropies Estimation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/f70k3m91er2qs",
  "venue": "arXiv",
  "versions": []
}