{
  "annotation_id": "9c760797-854a-4e77-bed1-d63856c94a35",
  "date_created": "2026-03-02T18:01:48.616000Z",
  "date_modified": "2026-03-02T18:01:48.616000Z",
  "file_hash": "dc390ecba9721740aec9a17c0b7867843bfd7e1f4b09ac0f271a68b843bd7beb",
  "private": false,
  "record": {
    "abstract": "We investigate the difference between classical and quantum dynamics of\ncoupled magnetic dipoles. We prove that in general the dynamics of the\nclassical interaction Hamiltonian differs from the corresponding quantum model,\nregardless of the initial state. The difference appears as non\npositive-definite diffusion terms in the quantum evolution equation of an\nappropriate positive phase-space probability density. Thus, it is not possible\nto express the dynamics in terms of a convolution of a positive transition\nprobability function and the initial condition as can be done in the classical\ncase. We conclude that the dynamics is a quantum element of NMR quantum\ninformation processing. There are two limits where our quantum evolution\ncoincide with the classical one: the short time limit before spin-spin\ninteraction sets in and the long time limit when phase diffusion is\nincorporated.",
    "arxiv_id": "quant-ph/0112001",
    "authors": [
      "G. J. Milburn",
      "R. Laflamme",
      "B. C. Sanders",
      "E. Knill"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.65.032316",
    "journal_ref": "Physical Review A 65(3), 032316 (2002)",
    "title": "The quantum dynamics of two coupled qubits",
    "url": "https://arxiv.org/abs/quant-ph/0112001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d4a6cead-59c8-4118-b393-c295c05a450d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}