{
  "annotation_id": "ba30b63c-c658-4549-8136-db110b3a1f7f",
  "date_created": "2026-03-02T18:02:10.445000Z",
  "date_modified": "2026-03-02T18:02:10.445000Z",
  "file_hash": "20de6bdbd6946a5cb2dee30fd1cbbe021e45f20a2eee7246dc6fa8e010028475",
  "private": false,
  "record": {
    "abstract": "Mutually unbiased bases generalize the X, Y and Z qubit bases. They possess\nnumerous applications in quantum information science. It is well-known that in\nprime power dimensions N=p^m (with p prime and m a positive integer) there\nexists a maximal set of N+1 mutually unbiased bases.\n  In the present paper, we derive an explicit expression for those bases, in\nterms of the (operations of the) associated finite field (Galois division ring)\nof N elements. This expression is shown to be equivalent to the expressions\npreviously obtained by Ivanovic in odd prime dimensions (J. Phys. A, 14, 3241\n(1981)), and Wootters and Fields (Ann. Phys. 191, 363 (1989)) in odd prime\npower dimensions. In even prime power dimensions, we derive a new explicit\nexpression for the mutually unbiased bases. The new ingredients of our approach\nare, basically, the following: we provide a simple expression of the\ngeneralised Pauli group in terms of the additive characters of the field and we\nderive an exact groupal composition law inside the elements of the commuting\nsubsets of the generalised Pauli group, renormalised by a well-chosen\nphase-factor.",
    "arxiv_id": "quant-ph/0409090",
    "authors": [
      "Thomas Durt"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "A new expression for mutually unbiased bases in prime power dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0409090"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1a8b8a35-c35e-4899-8c67-9d854cae1c85",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}