{
  "abstract": "Certifying a quantum bound can require more information than realizing the correlations that attain it. We show that this distinction becomes unbounded when a proof must condition on one party's measurement question. A fixed Bell scenario attained by one entangled qubit pair has a standard degree-two sum-of-squares certificate, yet the minimum degree in either conditioning direction grows as the inverse square root of the distance to a local endpoint. Choosing the better party does not remove this cost. The obstruction also survives approximate certification: bounding the quantum maximum to any fixed fractional accuracy relative to its Bell advantage requires the same diverging level. Thus a short standard proof cannot be transferred to a uniformly bounded conditioned level, even after relaxing exactness and optimising the direction. Mixing directions within a proof removes this family's obstruction, while a separate finite separation establishes its limits. Contact geometry explains the cost and connects it to a sharp precision law for randomness certification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10162",
  "author_total": 1,
  "authors": [
    {
      "name": "Fumin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/26hp90stz8gq6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10162",
  "fulltext_url": null,
  "id": "26hp90stz8gq6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10162",
  "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 Information and Cryptography"
    ]
  ],
  "openalex": "W7212191064",
  "pdf_url": "https://arxiv.org/pdf/2609.10162",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/26hp90stz8gq6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2609.10162",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10162"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The cost of direction in quantum Bell certification",
  "title_text": "The cost of direction in quantum Bell certification",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/26hp90stz8gq6",
  "venue": "arXiv",
  "versions": []
}