{
  "annotation_id": "6809e147-5058-46b5-82f6-89075ecc422b",
  "date_created": "2026-03-02T18:02:44.541000Z",
  "date_modified": "2026-03-02T18:02:44.541000Z",
  "file_hash": "0ffe389a9e1b6c7293755f70f8d96539dba75e37122360fb0e948656332909dd",
  "private": false,
  "record": {
    "abstract": "The search operation for a marked state by means of Grover\u0027s quantum\nsearching algorithm is shown to be an element of group SU(2) which acts on a\n2-dimensional space spanned by the marked state and the unmarked collective\nstate. Based on this underlying structure, those exact bounds of the steps in\nvarious quantum search algorithms are obtained in a quite concise way. This\nreformulation of the quantum searching algorithm also enables a detailed\nanalysis of the decoherence effects caused by its coupling with an environment.\nIt turns out that the environment will not only make the quantum search invalid\nin case of complete decoherence, where the probability of finding the marked\nstate is unchanged, but also it may make the quantum search algorithm worse\nthan expected: It will decrease this probability when the environment shows its\nquantum feature.",
    "arxiv_id": "quant-ph/9903075",
    "authors": [
      "Sixia Yu",
      "Chang-Pu Sun"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum searching\u0027s underlying SU(2) structure and its quantum   decoherence effects",
    "url": "https://arxiv.org/abs/quant-ph/9903075"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "11cfa45d-a3d4-4467-ade2-02898289230f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}