{
  "annotation_id": "c2f66222-83c3-4218-aa20-6debc56c3970",
  "date_created": "2026-03-02T18:02:44.262000Z",
  "date_modified": "2026-03-02T18:02:44.262000Z",
  "file_hash": "00fcbb45241f3702bd32234b29bb98d636182067a17ad84d232738c12e7bb6f8",
  "private": false,
  "record": {
    "abstract": "We consider the problem of how to manipulate the entanglement properties of a\ngeneral two-particle pure state, shared between Alice and Bob, by using only\nlocal operations at each end and classical communication between Alice and Bob.\nA method is developed in which this type of problem is found to be equivalent\nto a problem involving the cutting and pasting of certain shapes along with a\ncertain colouring problem. We consider two problems. Firstly we find the most\ngeneral way of manipulating the state to obtain maximally entangled states.\nAfter such a manipulation the entangled state |11\u003e+|22\u003e+....|mm\u003e is obtained\nwith probability p_m. We obtain an expression for the optimal average\nentanglement. Also, some results of Lo and Popescu pertaining to this problem\nare given simple geometric proofs. Secondly, we consider how to manipulate one\ntwo particle entangled pure state to another with certainty. We derive\nNielsen\u0027s theorem (which states the necessary and sufficient condition for this\nto be possible) using the method of areas.",
    "arxiv_id": "quant-ph/9903001",
    "authors": [
      "Lucien Hardy"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.60.1912",
    "title": "A Method of Areas for Manipulating the Entanglement Properties of One   Copy of a Two-Particle Pure State",
    "url": "https://arxiv.org/abs/quant-ph/9903001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b47accc9-6651-4cdf-9fb6-09b3ac999323",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}