{
  "abstract": "We give a proof of the cubic parallel-repetition bound for finite two-player entangled games using quantum conditional relative entropy. For a game with entangled value $1-\\varepsilon<1$ and answer alphabets $\\mathcal A,\\mathcal B$, its $n$-fold repeated value is at most \\[ \\exp[-Ω(\\varepsilon^3n/L)],\\qquad L:=\\max\\{1,\\log(|\\mathcal A||\\mathcal B|)\\}, \\] for every $n\\ge1$. This recovers Song's cubic rate. We also prove a threshold bound: the probability of winning a fraction at least $1-\\varepsilon+δ$ is at most $\\exp[-Ω(δ^5n/(\\varepsilon^2L))]$ for $0<δ\\le\\varepsilon$. Our information charge is the decrease in relative entropy when a question reference is discarded. Our comparison states preserve the original conditional question law. A chain rule bounds the coordinate charges using the cost of conditioning on checked wins and retaining checked answers. Our main lemma converts small charges into nearby pure-state descriptions and local corrections, each depending only on one player's question. Together with Song's sampler, these enable approximate local preparation of the conditioned workspace.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21410",
  "author_total": 1,
  "authors": [
    {
      "name": "Rahul Jain"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hdy485ttpzt2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21410",
  "fulltext_url": null,
  "id": "6hdy485ttpzt2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21410",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
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      "arxiv",
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    ],
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      "arxiv",
      "math.IT"
    ],
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      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
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  "openalex": "W7222516691",
  "pdf_url": "https://arxiv.org/pdf/2610.21410",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hdy485ttpzt2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21410",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21410"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Parallel Repetition for Entangled Games via Conditional Relative Entropy",
  "title_text": "Parallel Repetition for Entangled Games via Conditional Relative Entropy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/6hdy485ttpzt2",
  "venue": "arXiv",
  "versions": []
}