{
  "annotation_id": "f754c842-fbc0-4e5a-a56f-9932a84639ca",
  "date_created": "2026-03-02T18:02:27.562000Z",
  "date_modified": "2026-03-02T18:02:27.562000Z",
  "file_hash": "eb2fdc518bd66d6f567ac3b11faeeaa33a33572f7ddabfd566f37eff3476de60",
  "private": false,
  "record": {
    "abstract": "1-qubit quantum states form a space called the three-dimensional Bloch ball.\nTo compute Holevo capacity, Voronoi diagrams in the Bloch ball with respect to\nthe quantum divergence have been used as a powerful tool. These diagrams\nbasically treat mixed quantum states corresponding to points in the interior of\nthe Bloch ball. Due to the existence of logarithm in the quantum divergence,\nthe diagrams are not defined on pure quantum states corresponding to points on\nthe two-dimensional sphere. This paper first defines the Voronoi diagrams for\npure quantum states on the Bloch sphere by the Fubini-Study distance and the\nBures distance. We also introduce other Voronoi diagrams on the sphere obtained\nby taking a limit of Voronoi diagrams for mixed quantum states by the quantum\ndivergences in the Bloch ball. These diagrams are shown to be equivalent to the\nordinary Voronoi diagram on the sphere.",
    "arxiv_id": "quant-ph/0604101",
    "authors": [
      "Kimikazu Kato",
      "Mayumi Oto",
      "Hiroshi Imai",
      "Keiko Imai"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Voronoi Diagrams for Pure 1-qubit Quantum States",
    "url": "https://arxiv.org/abs/quant-ph/0604101"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "41348fba-e4a5-4353-8f1f-6ff66deb1448",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}