{
  "abstract": "We establish an equivalence between matrix samplers and quantum-proof randomness extractors. The classical sampler--extractor equivalence is established by a seminal work of Zuckerman (Random Structures & Algorithms, 1997). Using this equivalence, we construct explicit strong matrix samplers with optimal randomness overhead and near-optimal sample complexity via constructing quantum-proof extractors. Specifically for matrix dimension $D$, accuracy $\\varepsilon$ and failure probability $δ\\leq\\varepsilon$, our matrix sampler uses $m+O_α(\\log(D/δ))$ random bits and $O_α(\\varepsilon^{-2-α}\\log^{1+α}(D/δ))$ samples, for any constant $α>0$. Compared with the matrix sampler of Xun and Zuckerman (CCC 2025), our construction has improvements in two aspects. Under the same optimal random seed length, we can replace the $\\operatorname{poly} D$ dependence in the number of samples by $O(\\log^{1-γ} D)$. Under the same scale of sample size, we can remove their $\\log\\log D$ factor in the length of the random seed. Our underlying strong quantum-proof extractor has output length $n-O_α(a+\\log(1/η))$ and seed length at most $(1+α)\\log a+(2+α)\\log(1/η)+O_α(1)$ for $n$-bit sources with conditional min-entropy $n-a$ and error $η$. We also obtain strong quantum-proof extractors for every constant entropy rate, for any error as small as $2^{-Ω(n)}$, having optimal seed length $O(\\log(n/η))$ and output length $Ω(n)$, improving previous constructions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37122",
  "author_total": 2,
  "authors": [
    {
      "name": "Kuan Cheng"
    },
    {
      "name": "Ruiyang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8w5fkxpngrxh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37122",
  "fulltext_url": null,
  "id": "a8w5fkxpngrxh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37122",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7224134153",
  "pdf_url": "https://arxiv.org/pdf/2610.37122",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8w5fkxpngrxh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.37122",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37122"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Matrix Samplers and Quantum-Proof Extractors: Their Correspondence and Almost-Optimal Constructions",
  "title_text": "Matrix Samplers and Quantum-Proof Extractors: Their Correspondence and Almost-Optimal Constructions",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:04Z",
  "url": "https://research.draconitic.com/paper/a8w5fkxpngrxh",
  "venue": "arXiv",
  "versions": []
}