{
  "annotation_id": "1795a5c7-ccc4-43a8-a49e-7dbdba066054",
  "date_created": "2026-03-02T18:02:31.028000Z",
  "date_modified": "2026-03-02T18:02:31.028000Z",
  "file_hash": "7d5576ff64813ac767287a9adfec230569b7fc8290bb06964e3d361c1617adcb",
  "private": false,
  "record": {
    "abstract": "Randomization of quantum states is the quantum analogue of the classical\none-time pad. We present an improved, efficient construction of an\napproximately randomizing map that uses O(d/epsilon^2) Pauli operators to map\nany d-dimensional state to a state that is within trace distance epsilon of the\ncompletely mixed state. Our bound is a log d factor smaller than that of\nHayden, Leung, Shor, and Winter (2004), and Ambainis and Smith (2004).\n  Then, we show that a random sequence of essentially the same number of\nunitary operators, chosen from an appropriate set, with high probability form\nan approximately randomizing map for d-dimensional states. Finally, we discuss\nthe optimality of these schemes via connections to different notions of\npseudorandomness, and give a new lower bound for small epsilon.",
    "arxiv_id": "quant-ph/0611033",
    "authors": [
      "Paul A. Dickinson",
      "Ashwin Nayak"
    ],
    "categories": [
      "quant-ph",
      "cs.CR"
    ],
    "doi": "10.1063/1.2400876",
    "title": "Approximate Randomization of Quantum States With Fewer Bits of Key",
    "url": "https://arxiv.org/abs/quant-ph/0611033"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cb8d4eca-dfb1-4b6d-815b-27cdae301efa",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}