{
  "annotation_id": "2c8ca6a3-8499-4d40-9e0d-ffcf6918642f",
  "date_created": "2026-03-02T18:02:34.318000Z",
  "date_modified": "2026-03-02T18:02:34.318000Z",
  "file_hash": "f812f8ecdba94cc22382536044f8645f40fcdb80d82ffb9cd79a4a689830c517",
  "private": false,
  "record": {
    "abstract": "We introduce the problem of constructing weighted complex projective\n2-designs from the union of a family of orthonormal bases. If the weight\nremains constant across elements of the same basis, then such designs can be\ninterpreted as generalizations of complete sets of mutually unbiased bases,\nbeing equivalent whenever the design is composed of d+1 bases in dimension d.\nWe show that, for the purpose of quantum state determination, these designs\nspecify an optimal collection of orthogonal measurements. Using highly\nnonlinear functions on abelian groups, we construct explicit examples from d+2\northonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10,\nand 12, for example, where no complete sets of mutually unbiased bases have\nthus far been found.",
    "arxiv_id": "quant-ph/0703025",
    "authors": [
      "Aidan Roy",
      "A. J. Scott"
    ],
    "categories": [
      "quant-ph",
      "math.CO"
    ],
    "doi": "10.1063/1.2748617",
    "journal_ref": "J. Math. Phys. 48, 072110 (2007)",
    "title": "Weighted complex projective 2-designs from bases: optimal state   determination by orthogonal measurements",
    "url": "https://arxiv.org/abs/quant-ph/0703025"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9d420493-2027-4e81-854b-b70b38642033",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}