{
  "annotation_id": "206fb17d-e735-49c2-8ab2-66614b668fae",
  "date_created": "2026-03-02T18:02:20.733000Z",
  "date_modified": "2026-03-02T18:02:20.733000Z",
  "file_hash": "f9867165db74e9223095b9e89a3439530dbd16a5c22a67b63b772d4c4135d75d",
  "private": false,
  "record": {
    "abstract": "We introduce an interference measure which allows to quantify the amount of\ninterference present in any physical process that maps an initial density\nmatrix to a final density matrix. In particular, the interference measure\nenables one to monitor the amount of interference generated in each step of a\nquantum algorithm. We show that a Hadamard gate acting on a single qubit is a\nbasic building block for interference generation and realizes one bit of\ninterference, an ``i-bit\u0027\u0027. We use the interference measure to quantify\ninterference for various examples, including Grover\u0027s search algorithm and\nShor\u0027s factorization algorithm. We distinguish between ``potentially\navailable\u0027\u0027 and ``actually used\u0027\u0027 interference, and show that for both\nalgorithms the potentially available interference is exponentially large.\nHowever, the amount of interference actually used in Grover\u0027s algorithm is only\nabout 3 i-bits and asymptotically independent of the number of qubits, while\nShor\u0027s algorithm indeed uses an exponential amount of interference.",
    "arxiv_id": "quant-ph/0510159",
    "authors": [
      "Daniel Braun",
      "Bertrand Georgeot"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.mes-hall",
      "nlin.CD"
    ],
    "doi": "10.1103/PhysRevA.73.022314",
    "journal_ref": "Phys. Rev. A 73, 022314 (2006)",
    "title": "A Quantitative Measure of Interference",
    "url": "https://arxiv.org/abs/quant-ph/0510159"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1b7e889a-3827-45f4-bdd8-73fe32428172",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}