{
  "annotation_id": "419a8c9b-30e2-40a2-8008-06881bf6b521",
  "date_created": "2026-03-02T18:01:46.134000Z",
  "date_modified": "2026-03-02T18:01:46.134000Z",
  "file_hash": "74a51159f626e9fc785db9b1ec27fc6debc0b066ef5f17ab324da1ba844383c1",
  "private": false,
  "record": {
    "abstract": "We discuss the question of the existence of quantum one-way permutations.\nFirst, we prove the equivalence between inverting a permutation and that of\nconstructing a polynomial size network for reflecting about a given quantum\nstate. Next, we consider the question: if a state is difficult to prepare, is\nthe operator reflecting about that state difficult to construct? By revisiting\nGrover\u0027s algorithm, we present the relationship between this question and the\nexistence of one-way permutations. Moreover, we compare our method to Grover\u0027s\nalgorithm and discuss possible applications of our results.",
    "arxiv_id": "quant-ph/0109157",
    "authors": [
      "Elham Kashefi",
      "Harumichi Nishimura",
      "Vlatko Vedral"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "A note on quantum one-way permutations",
    "url": "https://arxiv.org/abs/quant-ph/0109157"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ac777f55-be88-41ba-9a20-c0868bff7926",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}