{
  "annotation_id": "5a602d8d-4a93-4fae-ba77-4c36966c4520",
  "date_created": "2026-03-02T18:02:20.657000Z",
  "date_modified": "2026-03-02T18:02:20.657000Z",
  "file_hash": "f4167726778f536eb64b87f7c2f929cd9656ceacae10666576f86f0b93050d81",
  "private": false,
  "record": {
    "abstract": "This paper deals with graph colouring games, an example of pseudo-telepathy,\nin which two provers can convince a verifier that a graph $G$ is $c$-colourable\nwhere $c$ is less than the chromatic number of the graph. They win the game if\nthey convince the verifier. It is known that the players cannot win if they\nshare only classical information, but they can win in some cases by sharing\nentanglement. The smallest known graph where the players win in the quantum\nsetting, but not in the classical setting, was found by Galliard, Tapp and Wolf\nand has 32,768 vertices. It is a connected component of the Hadamard graph\n$G_N$ with $N=c=16$. Their protocol applies only to Hadamard graphs where $N$\nis a power of 2. We propose a protocol that applies to all Hadamard graphs.\nCombined with a result of Frankl, this shows that the players can win on any\ninduced subgraph of $G_{12}$ having 1609 vertices, with $c=12$. Combined with a\nresult of Frankl and Rodl, our result shows that all sufficiently large\nHadamard graphs yield pseudo-telepathy games.",
    "arxiv_id": "quant-ph/0509047",
    "authors": [
      "David Avis",
      "Jun Hasegawa",
      "Yosuke Kikuchi",
      "Yuuya Sasaki"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1093/ietfec/e89-a.5.1378",
    "title": "A quantum protocol to win the graph colouring game on all Hadamard   graphs",
    "url": "https://arxiv.org/abs/quant-ph/0509047"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d0a589a8-e3e7-4592-9bbc-fbeed2559740",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}