{
  "annotation_id": "6c206404-1543-4ec2-a82d-f0620e6281ae",
  "date_created": "2026-03-02T18:01:35.762000Z",
  "date_modified": "2026-03-02T18:01:35.762000Z",
  "file_hash": "362673bdd7e3f79bbd5eebfb4029cad462d0737eb33802a38abd48a2db917a2e",
  "private": false,
  "record": {
    "abstract": "The concept of the {\\em half density matrix} is proposed. It unifies the\nquantum states which are described by density matrices and physical processes\nwhich are described by completely positive maps. With the help of the\nhalf-density-matrix representation of Hermitian linear map, we show that every\npositive map which is not completely positive is a {\\em difference} of two\ncompletely positive maps. A necessary and sufficient condition for a positive\nmap which is not completely positive is also presented, which is illustrated by\nsome examples.",
    "arxiv_id": "quant-ph/0001053",
    "authors": [
      "Sixia Yu"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.62.024302",
    "title": "Positive Maps Which Are Not Completely Positive",
    "url": "https://arxiv.org/abs/quant-ph/0001053"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0ebf4bcb-2b40-4691-ae97-59ef4677c83a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}