{
  "annotation_id": "46065eff-ee6b-4013-b51d-3a653cd4f1eb",
  "date_created": "2026-03-02T18:02:44.842000Z",
  "date_modified": "2026-03-02T18:02:44.842000Z",
  "file_hash": "086c556af3cf3edfef7f8877f5801b21aa0aa10df799db8f07373460abbc114d",
  "private": false,
  "record": {
    "abstract": "It is not a problem to complement a classical bit, i.e. to change the value\nof a bit, a 0 to a 1 and vice versa. This is accomplished by a NOT gate.\nComplementing a qubit in an unknown state, however, is another matter. We show\nthat this operation cannot be done perfectly. We define the Universal-NOT\n(U-NOT) gate which out of N identically prepared pure input qubits generates M\noutput qubits in a state which is as close as possible to the perfect\ncomplement. This gate can be realized by classical estimation and subsequent\nre-preparation of complements of the estimated state. Its fidelity is therefore\nequal to the fidelity F= (N+1)/(N+2) of optimal estimation, and does not depend\non the required number of outputs. We also show that when some additional a\npriori information about the state of input qubit is available, than the\nfidelity of the quantum NOT gate can be much better than the fidelity of\nestimation.",
    "arxiv_id": "quant-ph/9901053",
    "authors": [
      "V. Buzek",
      "M. Hillery",
      "R. Werner"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Optimal Manipulations with Qubits: Universal NOT Gate",
    "url": "https://arxiv.org/abs/quant-ph/9901053"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a30f8605-21da-4882-92da-40a89bbdbb16",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}