{
  "annotation_id": "c20d6118-68fc-406a-baa9-b0275e13de34",
  "date_created": "2026-03-02T18:02:03.064000Z",
  "date_modified": "2026-03-02T18:02:03.064000Z",
  "file_hash": "bea61313a6d503f1ae8cdefa90436a88fa32ea5f6129055cfd68eb801187ec84",
  "private": false,
  "record": {
    "abstract": "A mixed quantum state shared between two parties is said to be distillable\nif, by means of a protocol involving only local quantum operations and\nclassical communication, the two parties can transform some number of copies of\nthat state into a single shared pair of qubits having high fidelity with a\nmaximally entangled state state. In this paper it is proved that there exist\nstates that are distillable, but for which an arbitrarily large number of\ncopies is required before any distillation procedure can produce a shared pair\nof qubits with even a small amount of entanglement. Specifically, for every\npositive integer n there exists a state that is distillable, but given n or\nfewer copies of that state every distillation procedure outputting a single\nshared pair of qubits will output those qubits in a separable state.\nEssentially all previous examples of states proved to be distillable were such\nthat some distillation procedure could output an entangled pair of qubits given\na single copy of the state in question.",
    "arxiv_id": "quant-ph/0312123",
    "authors": [
      "John Watrous"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.93.010502",
    "title": "Many copies may be required for entanglement distillation",
    "url": "https://arxiv.org/abs/quant-ph/0312123"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3b928ddc-20d1-45ec-aa70-c8bfe15ebca1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}