{
  "annotation_id": "4a9f54b3-8d45-46b6-b53e-ac17e043d2b4",
  "date_created": "2026-03-02T18:02:13.326000Z",
  "date_modified": "2026-03-02T18:02:13.326000Z",
  "file_hash": "dd45bd06b1b4273bf3a9af704ee70121627c85bd3538ab6ff5f4787279575e04",
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  "record": {
    "abstract": "Mutually unbiased bases of a Hilbert space can be constructed by partitioning\na unitary error basis. We consider this construction when the unitary error\nbasis is a nice error basis. We show that the number of resulting mutually\nunbiased bases can be at most one plus the smallest prime power contained in\nthe dimension, and therefore that this construction cannot improve upon\nprevious approaches. We prove this by establishing a correspondence between\nnice mutually unbiased bases and abelian subgroups of the index group of a nice\nerror basis and then bounding the number of such subgroups. This bound also has\nimplications for the construction of certain combinatorial objects called nets.",
    "arxiv_id": "quant-ph/0412066",
    "authors": [
      "Michael Aschbacher",
      "Andrew M. Childs",
      "Pawel Wocjan"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10801-006-0002-y",
    "journal_ref": "Journal of Algebraic Combinatorics, Vol. 25, No. 2 (2007) 111-123",
    "title": "The limitations of nice mutually unbiased bases",
    "url": "https://arxiv.org/abs/quant-ph/0412066"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bebeb8f7-f3f1-4dbc-ae0e-e0765f157da0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}