{
  "annotation_id": "8b24e721-0f4e-4386-a811-9dab1893984b",
  "date_created": "2026-03-02T18:02:48.306000Z",
  "date_modified": "2026-03-02T18:02:48.306000Z",
  "file_hash": "ead6f1bd7b29e63e74f1dc088eedfc1ee208d75e25a44759b8b576a7e59035ec",
  "private": false,
  "record": {
    "abstract": "Purification is a process in which decoherence is partially reversed by using\nseveral input systems which have been subject to the same noise. The purity of\nthe outputs generally increases with the number of input systems, and decreases\nwith the number of required output systems. We construct the optimal quantum\noperations for this task, and discuss their asymptotic behaviour as the number\nof inputs goes to infinity. The rate at which output systems may be generated\ndepends crucially on the type of purity requirement. If one tests the purity of\nthe outputs systems one at a time, the rate is infinite: this fidelity may be\nmade to approach 1, while at the same time the number of outputs goes to\ninfinity arbitrarily fast. On the other hand, if one also requires the\ncorrelations between outputs to decrease, the rate is zero: if fidelity with\nthe pure product state is to go to 1, the number of outputs per input goes to\nzero. However, if only a fidelity close to 1 is required, the optimal purifier\nachieves a positive rate, which we compute.",
    "arxiv_id": "quant-ph/9910124",
    "authors": [
      "M. Keyl",
      "R. F. Werner"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The Rate of Optimal Purification procedures",
    "url": "https://arxiv.org/abs/quant-ph/9910124"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "82282fe7-e869-4fb7-979a-9f1b949ea22b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}