{
  "annotation_id": "b9af4451-4050-4592-9f18-253718269f38",
  "date_created": "2026-03-02T18:01:56.377000Z",
  "date_modified": "2026-03-02T18:01:56.377000Z",
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  "record": {
    "abstract": "A parameterization of the density operator, a coherence vector\nrepresentation, which uses a basis of orthogonal, traceless, Hermitian matrices\nis discussed. Using this parameterization we find the region of permissible\nvectors which represent a density operator. The inequalities which specify the\nregion are shown to involve the Casimir invariants of the group. In particular\ncases, this allows the determination of degeneracies in the spectrum of the\noperator. The identification of the Casimir invariants also provides a method\nof constructing quantities which are invariant under {\\it local} unitary\noperations. Several examples are given which illustrate the constraints\nprovided by the positivity requirements and the utility of the coherence vector\nparameterization.",
    "arxiv_id": "quant-ph/0302024",
    "authors": [
      "Mark S. Byrd",
      "Navin Khaneja"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.68.062322",
    "journal_ref": "PRA 68, 062322 (2003)",
    "title": "Characterization of the Positivity of the Density Matrix in Terms of the   Coherence Vector Representation",
    "url": "https://arxiv.org/abs/quant-ph/0302024"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "76f8265f-bc99-4c9b-91a3-0c4fd0e6ba8d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}