{
  "annotation_id": "e13ef92c-3c99-42cf-b813-a7e1a265f7b9",
  "date_created": "2026-03-02T18:02:27.176000Z",
  "date_modified": "2026-03-02T18:02:27.176000Z",
  "file_hash": "947af6d1ece0722425f9a48e567b1b4b08a692c9a73c5e07f4ef555696916e81",
  "private": false,
  "record": {
    "abstract": "For one-qubit pure quantum states, it is already proved that the Voronoi\ndiagrams with respect to two distances -- Euclidean distance and the quantum\ndivergence -- coincide. This fact is a support for a known method to calculate\nthe Holevo capacity. To consider an applicability of this method to quantum\nstates of a higher level system, it is essential to check if the coincidence of\nthe Voronoi diagrams also occurs. In this paper, we show a negative result for\nthat expectation. In other words, we mathematically prove that those diagrams\nno longer coincide in a higher dimension. That indicates that the method used\nin one-qubit case to calculate the Holevo capacity might not be effective in a\nhigher dimension.",
    "arxiv_id": "quant-ph/0607029",
    "authors": [
      "Kimikazu Kato",
      "Mayumi Oto",
      "Hiroshi Imai",
      "Keiko Imai"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On a Geometric Structure of Pure Multi-qubit Quantum States and Its   Applicability to a Numerical Computation",
    "url": "https://arxiv.org/abs/quant-ph/0607029"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0cd5399f-ec6a-44d7-b9ef-5f09cafc7272",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}