{
  "annotation_id": "67614adf-2942-46fa-938a-7ecf65a9ad9e",
  "date_created": "2026-03-02T18:02:10.288000Z",
  "date_modified": "2026-03-02T18:02:10.288000Z",
  "file_hash": "cd106359372eeb914246abeaadd173c8f0f20ca1da15ef8537ec979f8eeedc0a",
  "private": false,
  "record": {
    "abstract": "We show that k=w+2 mutually unbiased bases can be constructed in any square\ndimension d=s^2 provided that there are w mutually orthogonal Latin squares of\norder s. The construction combines the design-theoretic objects (k,s)-nets\n(which can be constructed from w mutually orthogonal Latin squares of order s\nand vice versa) and generalized Hadamard matrices of size s. Using known lower\nbounds on the asymptotic growth of the number of mutually orthogonal Latin\nsquares (based on number theoretic sieving techniques), we obtain that the\nnumber of mutually unbiased bases in dimensions d=s^2 is greater than s^1/14.8\nfor all s but finitely many exceptions. Furthermore, our construction gives\nmore mutually orthogonal bases in many non-prime-power dimensions than the\nconstruction that reduces the problem to prime power dimensions.",
    "arxiv_id": "quant-ph/0407081",
    "authors": [
      "Pawel Wocjan",
      "Thomas Beth"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "New Construction of Mutually Unbiased Bases in Square Dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0407081"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f970c201-09e4-4b67-84a4-831e2611dc79",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}