{
  "annotation_id": "907d81b8-f5d1-442d-b057-f87fce1fd886",
  "date_created": "2026-03-02T18:02:45.145000Z",
  "date_modified": "2026-03-02T18:02:45.145000Z",
  "file_hash": "9999c876fba454e592a5478de026e7730e45d27582a2495b61f933e4e122f5ef",
  "private": false,
  "record": {
    "abstract": "We give a constructive proof that all mixed states of N qubits in a\nsufficiently small neighborhood of the maximally mixed state are separable. The\nconstruction provides an explicit representation of any such state as a mixture\nof product states. We give upper and lower bounds on the size of the\nneighborhood, which show that its extent decreases exponentially with the\nnumber of qubits. We also discuss the implications of the bounds for NMR\nquantum computing.",
    "arxiv_id": "quant-ph/9811018",
    "authors": [
      "S. L. Braunstein",
      "C. M. Caves",
      "R. Jozsa",
      "N. Linden",
      "S. Popescu",
      "R. Schack"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.83.1054",
    "journal_ref": "Phys.Rev.Lett. 83 (1999) 1054-1057",
    "title": "Separability of very noisy mixed states and implications for NMR quantum   computing",
    "url": "https://arxiv.org/abs/quant-ph/9811018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0c01bb8c-c37b-4f18-b072-65c12c401658",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}