{
  "annotation_id": "88694664-b9d9-4bfb-8336-bf97c5a5259e",
  "date_created": "2026-03-02T18:02:48.097000Z",
  "date_modified": "2026-03-02T18:02:48.097000Z",
  "file_hash": "1d68d2993f04d2e4a1d0629a5bc74008494e4d13e85552e215a3a139cb97cf95",
  "private": false,
  "record": {
    "abstract": "We report new results and generalizations of our work on unextendible product\nbases (UPB), uncompletable product bases and bound entanglement. We present a\nnew construction for bound entangled states based on product bases which are\nonly completable in a locally extended Hilbert space. We introduce a very\nuseful representation of a product basis, an orthogonality graph. Using this\nrepresentation we give a complete characterization of unextendible product\nbases for two qutrits. We present several generalizations of UPBs to arbitrary\nhigh dimensions and multipartite systems. We present a sufficient condition for\nsets of orthogonal product states to be distinguishable by separable\nsuperoperators. We prove that bound entangled states cannot help increase the\ndistillable entanglement of a state beyond its regularized entanglement of\nformation assisted by bound entanglement.",
    "arxiv_id": "quant-ph/9908070",
    "authors": [
      "David P. DiVincenzo",
      "Tal Mor",
      "Peter W. Shor",
      "John A. Smolin",
      "Barbara M. Terhal"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s00220-003-0877-6",
    "journal_ref": "Comm. Math. Phys. 238, pp. 379--410 (2003)",
    "title": "Unextendible Product Bases, Uncompletable Product Bases and Bound   Entanglement",
    "url": "https://arxiv.org/abs/quant-ph/9908070"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "928eec90-fe9c-45c8-ad65-73bb305954a2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}