{
  "annotation_id": "fb9d9a3b-0162-411e-91d4-25cabb0cbf18",
  "date_created": "2026-03-02T18:02:45.247000Z",
  "date_modified": "2026-03-02T18:02:45.247000Z",
  "file_hash": "da2920723a1548a525ffa7835cdabfd7833e0e81f1546287ba70c2cebe492070",
  "private": false,
  "record": {
    "abstract": "Two families of bipartite mixed quantum states are studied for which it is\nproved that the number of members in the optimal-decomposition ensemble --- the\nensemble realizing the entanglement of formation --- is greater than the rank\nof the mixed state. We find examples for which the number of states in this\noptimal ensemble can be larger than the rank by an arbitrarily large factor. In\none case the proof relies on the fact that the partial transpose of the mixed\nstate has zero eigenvalues; in the other case the result arises from the\nproperties of product bases that are completable only by embedding in a larger\nHilbert space.",
    "arxiv_id": "quant-ph/9904005",
    "authors": [
      "David P. DiVincenzo",
      "Barbara M. Terhal",
      "Ashish V. Thapliyal"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1080/09500340008244049",
    "title": "Optimal Decompositions of Barely Separable States",
    "url": "https://arxiv.org/abs/quant-ph/9904005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "52ff9950-2753-4162-bce6-ad47ca87e7b3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}