{
  "annotation_id": "5e3c3751-2442-416e-9c7c-9a3358a4cb8b",
  "date_created": "2026-03-02T18:02:48.304000Z",
  "date_modified": "2026-03-02T18:02:48.304000Z",
  "file_hash": "2b0b140d4b4ce03aedb8a52843d34fd492aa47621b1b5953c0609cec15dd926b",
  "private": false,
  "record": {
    "abstract": "We explore the relation between the rank of a bipartite density matrix and\nthe existence of bound entanglement. We show a relation between the rank,\nmarginal ranks, and distillability of a mixed state and use this to prove that\nany rank n bound entangled state must have support on no more than an n \\times\nn Hilbert space. A direct consequence of this result is that there are no\nbipartite bound entangled states of rank two. We also show that a separability\ncondition in terms of a quantum entropy inequality is associated with the above\nresults. We explore the idea of how many pure states are needed in a mixture to\ncancel the distillable entanglement of a Schmidt rank n pure state and provide\na lower bound of n-1. We also prove that a mixture of a non-zero amount of any\npure entangled state with a pure product state is distillable.",
    "arxiv_id": "quant-ph/9910122",
    "authors": [
      "Pawel Horodecki",
      "John A. Smolin",
      "Barbara M. Terhal",
      "Ashish V. Thapliyal"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Rank Two Bipartite Bound Entangled States Do Not Exist",
    "url": "https://arxiv.org/abs/quant-ph/9910122"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a1f46012-de7b-44e2-9de8-82c02ce042ed",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}