{
  "abstract": "A binary $(n,m)$ quantum random access code (QRAC) compresses an $n$-bit classical string into an $m$-qubit quantum state, from which a decoder attempts to recover a randomly selected target bit. Of particular interest is the optimal average probability of success, $P^{Q,\\mathrm{avg},\\mathrm{opt}}_{n,m}$, which was numerically conjectured to satisfy the bound $P^{Q,\\mathrm{avg},\\mathrm{opt}}_{n,m}\\leq \\frac{1}{2}+\\frac{1}{2}\\sqrt{\\frac{m}{n}}$. Recent constructions of $(n,n-1)$ QRACs by Suzuki and $(n,n-2)$ QRACs by Akibue et al. meet this bound exactly, raising the question of their strict optimality. In this work, we settle this question by proving the conjectured upper bound for $m\\in\\{n-1,n-2\\}$, thereby precisely determining $P^{Q,\\mathrm{avg},\\mathrm{opt}}_{n,n-1}$ and $P^{Q,\\mathrm{avg},\\mathrm{opt}}_{n,n-2}$. The proof utilizes a translation recently studied by Lin and de Wolf from local to global reconstruction via pretty good measurement, along with dimensional and positive-semidefinite constraints on an induced channel.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.10414",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuo Tan"
    },
    {
      "name": "Syed A. Jafar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84p93h33f5hwv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.10414",
  "fulltext_url": null,
  "id": "84p93h33f5hwv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.10414",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7168256085",
  "pdf_url": "https://arxiv.org/pdf/2607.10414",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/84p93h33f5hwv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2607.10414",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.10414"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal Average Success Probabilities of Binary $(n,n-1)$ and $(n,n-2)$ Quantum Random Access Codes",
  "title_text": "Optimal Average Success Probabilities of Binary (n,n−1) and (n,n−2) Quantum Random Access Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/84p93h33f5hwv",
  "venue": "arXiv",
  "versions": []
}