{
  "annotation_id": "d77bf35c-72e9-4964-b75c-b18e776d3d27",
  "date_created": "2026-03-02T18:02:31.199000Z",
  "date_modified": "2026-03-02T18:02:31.199000Z",
  "file_hash": "079d5e5fe2b9a8e954bf57082e1d3a3c322db74f60970db7796e61597bb6166b",
  "private": false,
  "record": {
    "abstract": "We give a new geometric interpretation of quantum pure states. Using\n  Voronoi diagrams, we reinterpret the structure of the space of pure states as\na subspace of the quantum state space. In addition to the known coincidence of\nsome Voronoi diagrams for one-qubit pure states, we will show that even for\nmixed one-qubit states, as far as sites are given as pure states, the Voronoi\ndiagram with respect to some distances -- the divergence, the Bures distance,\nand the Euclidean distance -- are all the same.\n  As to higher level pure quantum states, for the divergence, the\n  Fubini-Study distance, and the Bures distance, the coincidence of the\ndiagrams still holds, while the coincidence of the diagrams with respect to the\ndivergence and the Euclidean distance no longer holds. That fact has a\nsignificant meaning when we try to apply the method used for a numerical\nestimation of a one-qubit quantum channel capacity to a higher level system.",
    "arxiv_id": "quant-ph/0611146",
    "authors": [
      "Kimikazu Kato",
      "Mayumi Oto",
      "Hiroshi Imai",
      "Keiko Imai"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Voronoi Diagrams and a Numerical Estimation of a Quantum Channel   Capacity",
    "url": "https://arxiv.org/abs/quant-ph/0611146"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "15128baa-ee44-4fef-86af-51eb035fb916",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}