{
  "annotation_id": "58c18a5a-56c9-4409-a311-46e64c2b8b88",
  "date_created": "2026-03-02T18:01:59.334000Z",
  "date_modified": "2026-03-02T18:01:59.334000Z",
  "file_hash": "0bc6571f080b69550ca9ebb1abc8009d00651058ad0181743f648b1fb0a63822",
  "private": false,
  "record": {
    "abstract": "This paper focuses on the geometric phase of general mixed states under\nunitary evolution. Here we analyze both non-degenerate as well as degenerate\nstates. Starting with the non-degenerate case, we show that the usual procedure\nof subtracting the dynamical phase from the total phase to yield the geometric\nphase for pure states, does not hold for mixed states. To this end, we furnish\nan expression for the geometric phase that is gauge invariant. The parallelity\nconditions are shown to be easily derivable from this expression. We also\nextend our formalism to states that exhibit degeneracies. Here with the\nholonomy taking on a non-abelian character, we provide an expression for the\ngeometric phase that is manifestly gauge invariant. As in the case of the\nnon-degenerate case, the form also displays the parallelity conditions clearly.\nFinally, we furnish explicit examples of the geometric phases for both the\nnon-degenerate as well as degenerate mixed states.",
    "arxiv_id": "quant-ph/0304068",
    "authors": [
      "K. Singh",
      "D. M. Tong",
      "K. Basu",
      "J. L. Chen",
      "J. F. Du"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.67.032106",
    "journal_ref": "PRA 67, 032106 (2003)",
    "title": "Geometric phases for non-degenerate and degenerate mixed states",
    "url": "https://arxiv.org/abs/quant-ph/0304068"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2484cfbf-cb16-498c-8adb-21f8285dde58",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}