{
  "annotation_id": "8fbb8371-bd00-45b2-9e10-c190bd945711",
  "date_created": "2026-03-02T18:01:51.847000Z",
  "date_modified": "2026-03-02T18:01:51.847000Z",
  "file_hash": "a4edcadc1c212fc4804d62b9b31c158a059a27c8debddaa6914ad1edd826fac5",
  "private": false,
  "record": {
    "abstract": "We prove that majorization relations hold step by step in the Quantum Fourier\nTransformation (QFT) for phase-estimation algorithms considered in the\ncanonical decomposition. Our result relies on the fact that states which are\nmixed by Hadamard operators at any stage of the computation only differ by a\nphase. This property is a consequence of the structure of the initial state and\nof the QFT, based on controlled-phase operators and a single action of a\nHadamard gate per qubit. As a consequence, Hadamard gates order the probability\ndistribution associated to the quantum state, whereas controlled-phase\noperators carry all the entanglement but are immaterial to majorization. We\nalso prove that majorization in phase-estimation algorithms follows in a most\nnatural way from unitary evolution, unlike its counterpart in Grover\u0027s\nalgorithm.",
    "arxiv_id": "quant-ph/0206134",
    "authors": [
      "Roman Orus",
      "Jose I. Latorre",
      "Miguel A. Martin-Delgado"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Quantum Information Processing 1 (4): 283-302 (2002)",
    "title": "Natural majorization of the Quantum Fourier Transformation in   phase-estimation algorithms",
    "url": "https://arxiv.org/abs/quant-ph/0206134"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "67c498b4-8cbf-4f5b-939d-b9fe145c5b8c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}