{
  "annotation_id": "63ec276c-4df8-45cf-be09-2afdee001ced",
  "date_created": "2026-03-02T18:01:48.278000Z",
  "date_modified": "2026-03-02T18:01:48.278000Z",
  "file_hash": "452b7d0165a2aa9b9fe670092378a7fe189533116e0ec55b836a4966415ca1ac",
  "private": false,
  "record": {
    "abstract": "It is shown that the set of rank r separable states is measure zero within\nthe set of low rank states provided r is less than an upper bound which depends\nupon the number of particles and the dimensions of the spaces they are modelled\non. The upper bound is given. In the bipartite case in which both particles are\nmodelled on m-dimensional hilbert space it is (m-1)^2. In the case of p qubits\nit is (2^p)-p. This paper is a corretion of one I recently posted and\nsubsequently withdrew. That paper claimed the set of rank r separable states is\nmeasure zero if r is non-maximal rank. That may be true, but the proof in the\nwithdrawn paper was false.",
    "arxiv_id": "quant-ph/0111051",
    "authors": [
      "Robert Lockhart"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.65.064304",
    "title": "Low rank separable states are a set of measure zero within the set of   low rank states",
    "url": "https://arxiv.org/abs/quant-ph/0111051"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "07b9fbb0-0344-4a92-bf68-77f3fdcba4a4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}