{
  "annotation_id": "98f99daa-e936-412e-a915-c24c49399c89",
  "date_created": "2026-03-02T18:02:09.392000Z",
  "date_modified": "2026-03-02T18:02:09.392000Z",
  "file_hash": "ff02103f7f46f4a92017cd6b90a8420f8fd815796c10e13ef2f123f637bba37c",
  "private": false,
  "record": {
    "abstract": "A completely entangled subspace of a tensor product of Hilbert spaces is a\nsubspace with no non-trivial product vector. K. R. Parthasarathy determined the\nmaximum dimension possible for such a subspace. Here we present a simple\nexplicit example of one such space. We determine the set of product vectors in\nits orthogonal complement and see that it spans whole of the orthogonal\ncomplement. This way we are able to determine the minimum dimension possible\nfor an unextendible product basis (UPB) consisting of product vectors which are\nlinearly independent but not necessarily mutually orthogonal.",
    "arxiv_id": "quant-ph/0409032",
    "authors": [
      "B. V. Rajarama Bhat"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/S0219749906001797",
    "journal_ref": "International Journal of Quantum Information, Vol. 04, No. 2,\n  325-330(2006)",
    "title": "A completely entangled subspace of maximal dimension",
    "url": "https://arxiv.org/abs/quant-ph/0409032"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b40035c1-b835-4bcc-a958-1615838d90bb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}