{
  "annotation_id": "45bbcd6c-fb7a-40e5-af7f-10b82e661d7a",
  "date_created": "2026-03-02T18:02:16.422000Z",
  "date_modified": "2026-03-02T18:02:16.422000Z",
  "file_hash": "f0f51da405914880effd14d4d9eda9275ab905fc828ae962970821bc42af8aa6",
  "private": false,
  "record": {
    "abstract": "In this paper we give a general integral representation for separable states\nin the tensor product of infinite dimensional Hilbert spaces and provide the\nfirst example of separable states that are not countably decomposable. We also\nprove the structure theorem for the quantum communication channels that are\nentanglement-breaking, generalizing the finite-dimensional result of M.\nHorodecki, Ruskai and Shor. In the finite dimensional case such channels can be\ncharacterized as having the\n  Kraus representation with operators of rank 1. The above example implies\nexistence of infinite-dimensional entanglement-breaking channels having no such\nrepresentation.",
    "arxiv_id": "quant-ph/0504204",
    "authors": [
      "A. S. Holevo",
      "M. E. Shirokov",
      "R. F. Werner"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Russian Math. Surveys, vol. 60, N2,2005",
    "title": "Separability and Entanglement-Breaking in Infinite Dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0504204"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "045201b0-f38a-45d9-b52a-d97f745dc12a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}