{
  "annotation_id": "5ad72396-7e6a-416f-a298-f342aead7510",
  "date_created": "2026-03-02T18:01:44.863000Z",
  "date_modified": "2026-03-02T18:01:44.863000Z",
  "file_hash": "2d7eb191f313a7d6fc266ac350e0c5a690e9389d6cd23fdab5b30740d10f6427",
  "private": false,
  "record": {
    "abstract": "Well-known Nuclear Magnetic Resonance experiments show that the time\nevolution according to (truncated) dipole-dipole interactions between n spins\ncan be inverted by simple pulse sequences. Independent of n, the reversed\nevolution is only two times slower than the original one. Here we consider more\ngeneral spin-spin couplings with long range. We prove that some are\nconsiderably more complex to invert since the number of required time steps and\nthe slow-down of the reversed evolutions are necessarily of the order n.\nFurthermore, the spins have to be addressed separately. We show for which\nvalues of the coupling parameters the phase transition between simple and\ncomplex time-reversal schemes occurs.",
    "arxiv_id": "quant-ph/0106085",
    "authors": [
      "Dominik Janzing",
      "Pawel Wocjan",
      "Thomas Beth"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.66.042311",
    "journal_ref": "Phys. Rev. A 66, 042311, 2002",
    "title": "Complexity of decoupling and time-reversal for n spins with   pair-interactions: Arrow of time in quantum control",
    "url": "https://arxiv.org/abs/quant-ph/0106085"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c11b4317-28f9-4c9c-8475-549c2b7fe87a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}