{
  "abstract": "We confirm a conjecture of the first author [SODA'26] on a strong form of pseudo-telepathy for Khot's $d$-to-$1$ games: for every $d\\geq 4$, every $ε>0$, and every $k\\in\\mathbb N$, there is a $d$-to-$1$ label-cover game of classical value less than $ε$ that admits a perfect quantum strategy using finite-dimensional shared entanglement with measurement contexts of radius at least $k$. As a consequence, there exist graphs whose quantum chromatic number $χ_q$ is $3$ and whose classical chromatic number $χ$ is arbitrarily large. This is the first improvement on the quantum chromatic gap since the work of Brassard, Cleve, and Tapp [Phys. Rev. Lett.'99], which produced graphs for which $χ$ grows exponentially in $χ_q$. To prove the conjecture, we proceed as follows. We start with a ``stretched'' version of the Mermin--Peres magic square, obtained by spacing out its equations and linking them with additional long equation wires. This operation increases the radius of the initial measurement contexts of a perfect quantum strategy for the game, while preserving classical unsatisfiability. We then apply parallel repetition to make the classical value small, and we turn the system into a pseudo-telepathic multi-layered Kneser hypergraph via a PCP construction of Dinur, Guruswami, Khot, and Regev [STOC'03]. Finally, we feed the resulting hypergraph into the reduction of Fei, Minzer, and Wang from hypergraph colouring to $4$-to-$1$ games, we establish quantum completeness of this reduction, and we show that it preserves context radius.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40571",
  "author_total": 2,
  "authors": [
    {
      "name": "Lorenzo Ciardo"
    },
    {
      "name": "Antoine Mottet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eg840k59r16ra.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40571",
  "fulltext_url": null,
  "id": "eg840k59r16ra",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40571",
  "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.CC"
    ],
    [
      "arxiv",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eg840k59r16ra.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40571"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "On the Quantum Chromatic Gap II",
  "title_text": "On the Quantum Chromatic Gap II",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:28Z",
  "url": "https://research.draconitic.com/paper/eg840k59r16ra",
  "venue": "arXiv",
  "versions": []
}