{
  "annotation_id": "00b893e5-60c4-4ab2-8d2c-0e5e00e7b3b4",
  "date_created": "2026-03-02T18:01:52.931000Z",
  "date_modified": "2026-03-02T18:01:52.931000Z",
  "file_hash": "8f75eff58942ea358d7b9f5b14fab3e075fe6035015e5b6e1e2c1732e6d9ab29",
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  "record": {
    "abstract": "Operator-Schmidt decompositions of the quantum Fourier transform on C^N1\ntensor C^N2 are computed for all N1, N2 \u003e 1. The decomposition is shown to be\ncompletely degenerate when N1 is a factor of N2 and when N1\u003eN2. The first known\nspecial case, N1=N2=2^n, was computed by Nielsen in his study of the\ncommunication cost of computing the quantum Fourier transform of a collection\nof qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis,\nUniversity of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More\ngenerally, the special case N1=2^n1\u003c2^n2=N2 was computed by Nielsen et. al. in\ntheir study of strength measures of quantum operations. [M.A. Nielsen et. al,\n(accepted for publication in Phys Rev A); arXiv:quant-ph/0208077.] Given the\nSchmidt decompositions presented here, it follows that in all cases the\ncommunication cost of exact computation of the quantum Fourier transform is\nmaximal.",
    "arxiv_id": "quant-ph/0210100",
    "authors": [
      "Jon Tyson"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/36/24/317",
    "journal_ref": "J. Phys. A: Math. Gen. 36 (2003) 6485-6491",
    "title": "Operator-Schmidt decomposition of the quantum Fourier transform on C^N1   tensor C^N2",
    "url": "https://arxiv.org/abs/quant-ph/0210100"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cbf0420f-99a1-4c5f-990c-09dcb2e2afa4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}