{
  "annotation_id": "66fea88f-67db-4e33-9e29-3738afbe0371",
  "date_created": "2026-03-02T18:02:12.915000Z",
  "date_modified": "2026-03-02T18:02:12.915000Z",
  "file_hash": "4a95c23f65791b6eba5ed72db3f8a675f7193209028067076eb313ffca7ec1c5",
  "private": false,
  "record": {
    "abstract": "We outline a new approach to the characterization as well as to the\nclassification of positive maps. This approach is based on the facial\nstructures of the set of states and of the cone of positive maps. In\nparticular, the equivalence between Schroedinger\u0027s and Heisenberg\u0027s pictures is\nreviewed in this more general setting. Furthermore, we discuss in detail the\nstructure of positive maps for two and three dimensional systems. In\nparticular, the explicit form of decomposition of a positive map and the\nuniqueness of this decomposition for extremal positive maps for 2 dimensional\ncase are described. The difference of the structure of positive maps between 2\ndimensional and 3 dimensional cases is clarified. The resulting\ncharacterization of positive maps is applied to the study of quantum\ncorrelations and entanglement",
    "arxiv_id": "quant-ph/0411043",
    "authors": [
      "Wladyslaw Adam Majewski"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Positive maps, states, entanglement and all that; some old and new   problems",
    "url": "https://arxiv.org/abs/quant-ph/0411043"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5b17d1b9-d240-498e-bf01-6529292e89ed",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}