{
  "annotation_id": "1843ebd6-9f16-4ce1-ab6d-a389b3e31123",
  "date_created": "2026-03-02T18:02:27.657000Z",
  "date_modified": "2026-03-02T18:02:27.657000Z",
  "file_hash": "1304246377a3d7c4efc85a64864f2a4a25059703d5ed3b610f9864e22c1aa3b7",
  "private": false,
  "record": {
    "abstract": "In the present paper, the trace distance is exposed within the quantum\noperations formalism. The definition of the trace distance in terms of a\nmaximum over all quantum operations is given. It is shown that for any pair of\ndifferent states, there are an uncountably infinite number of maximizing\nquantum operations. Conversely, for any operation of the described type, there\nare an uncountably infinite number of those pairs of states that the maximum is\nreached by the operation. A behavior of the trace distance under considered\noperations is studied. Relations and distinctions between the trace distance\nand the sine distance are discussed.",
    "arxiv_id": "quant-ph/0605172",
    "authors": [
      "A. E. Rastegin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/1751-8113/40/31/026",
    "journal_ref": "J. Phys. A: Math. Theor. 40 (2007) 9533-9549",
    "title": "Trace distance from the viewpoint of quantum operation techniques",
    "url": "https://arxiv.org/abs/quant-ph/0605172"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d2789787-b2b2-4a33-899f-91525ad79d58",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}