{
  "annotation_id": "5af4c646-fee9-4f91-a973-ec1d3ef8e268",
  "date_created": "2026-03-02T18:02:34.185000Z",
  "date_modified": "2026-03-02T18:02:34.185000Z",
  "file_hash": "2356261772decfc04d7c9bafb54579f5144c8eff10af2046f9a30389c8a5c868",
  "private": false,
  "record": {
    "abstract": "A Gleason-type theorem is proved for two restricted classes of\ninformationally complete POVMs in the qubit case. A particular (incomplete)\nKochen-Specker colouring, suggested by Appleby in dimension three, is\ngeneralized to arbitrary dimension. We investigate its effectivity as a\nfunction of dimension, using two different measures of this. In particular, we\nwill derive a limit for the fraction of the sphere that can be satisfactorily\ncoloured using the generalized Appleby construction as the number of dimensions\napproaches infinity. The second, and physically more relevant measure of\neffectivity, is to look at the fraction of possible ON-bases properly coloured.\nUsing this measure, we will derive a \u0027lower bound for the upper bound\u0027 in three\nand four real dimensions.",
    "arxiv_id": "quant-ph/0612103",
    "authors": [
      "Helena Granstrom"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Some remarks on the theorems of Gleason and Kochen-Specker",
    "url": "https://arxiv.org/abs/quant-ph/0612103"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "59b85736-018f-47a2-b47f-e656e543a7d1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}