{
  "annotation_id": "8a582eca-9288-4dcd-ba8a-5d513f23ac7e",
  "date_created": "2026-03-02T18:02:19.960000Z",
  "date_modified": "2026-03-02T18:02:19.960000Z",
  "file_hash": "4c68fc7cb2cc665bf17e93c5c9274342c477571d10cf9c7975a3a525adb0cdb0",
  "private": false,
  "record": {
    "abstract": "It is well known that n bits of entropy are necessary and sufficient to\nperfectly encrypt n bits (one-time pad). Even if we allow the encryption to be\napproximate, the amount of entropy needed doesn\u0027t asymptotically change.\nHowever, this is not the case when we are encrypting quantum bits. For the\nperfect encryption of n quantum bits, 2n bits of entropy are necessary and\nsufficient (quantum one-time pad), but for approximate encryption one\nasymptotically needs only n bits of entropy. In this paper, we provide the\noptimal trade-off between the approximation measure epsilon and the amount of\nclassical entropy used in the encryption of single quantum bits. Then, we\nconsider n-qubit encryption schemes which are a composition of independent\nsingle-qubit ones and provide the optimal schemes both in the 2- and the\noperator-norm. Moreover, we provide a counterexample to show that the\nencryption scheme of Ambainis-Smith based on small-bias sets does not work in\nthe operator-norm.",
    "arxiv_id": "quant-ph/0509169",
    "authors": [
      "Iordanis Kerenidis",
      "Daniel Nagaj"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.2339014",
    "journal_ref": "J. Math. Phys. 47, 092102 (2006)",
    "title": "On the Optimality of Quantum Encryption Schemes",
    "url": "https://arxiv.org/abs/quant-ph/0509169"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8b32b4e1-944f-48b5-9eb9-8f04f86f33b9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}