{
  "annotation_id": "0ff6513b-4cb8-467c-8bcc-d1509229f771",
  "date_created": "2026-03-02T18:01:59.754000Z",
  "date_modified": "2026-03-02T18:01:59.754000Z",
  "file_hash": "c49250777a7c65394e444909bbc54399186dee001a9c6c364fde1eb584bf3b16",
  "private": false,
  "record": {
    "abstract": "Grover\u0027s quantum search algorithm is analyzed for the case in which the\ninitial state is an arbitrary pure quantum state $|\\phi\u003e$ of $n$ qubits. It is\nshown that the optimal time to perform the measurement is independent of $|\n\\phi\u003e$, namely, it is identical to the optimal time in the original algorithm\nin which $| \\phi \u003e = | 0\u003e$, with the same number of marked states, $r$. The\nprobability of success $P_{\\rm s}$ is obtained, in terms of the amplitudes of\nthe state $| \\phi\u003e$, and is shown to be independent of $r$. A class of states,\nwhich includes fixed points and cycles of the Grover iteration operator is\nidentified. The relevance of these results in the context of using the success\nprobability as an entanglement measure is discussed. In particular, the\nGroverian entanglement measure, previously limited to a single marked state, is\ngeneralized to the case of several marked states.",
    "arxiv_id": "quant-ph/0307141",
    "authors": [
      "O. Biham",
      "D. Shapira",
      "Y. Shimoni"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.68.022326",
    "journal_ref": "Phys. Rev. A 68, 022326 (2003)",
    "title": "Analysis of Grover\u0027s quantum search algorithm as a dynamical system",
    "url": "https://arxiv.org/abs/quant-ph/0307141"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f2b632cb-fd7b-4859-bdea-fc8d5a4d9e48",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}