{
  "annotation_id": "35a8c252-dfd9-4370-8e9a-5dc27fe8215f",
  "date_created": "2026-03-02T18:01:41.720000Z",
  "date_modified": "2026-03-02T18:01:41.720000Z",
  "file_hash": "758a2d05492c2a250a7a1fc109fe323def3e8ab89f2be3ce0f3fc69aac946a07",
  "private": false,
  "record": {
    "abstract": "We develop a strong connection between maximally commuting bases of\northogonal unitary matrices and mutually unbiased bases. A necessary condition\nof the existence of mutually unbiased bases for any finite dimension is\nobtained. Then a constructive proof of the existence of mutually unbiased bases\nfor dimensions which are power of a prime is presented. It is also proved that\nin any dimension d the number of mutually unbiased bases is at most d+1. An\nexplicit representation of mutually unbiased observables in terms of Pauli\nmatrices are provided for d=2^m.",
    "arxiv_id": "quant-ph/0103162",
    "authors": [
      "Somshubhro Bandyopadhyay",
      "P. Oscar Boykin",
      "Vwani Roychowdhury",
      "Farrokh Vatan"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "A new proof for the existence of mutually unbiased bases",
    "url": "https://arxiv.org/abs/quant-ph/0103162"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "77fa1448-f68a-4bb3-8386-82c6af65a365",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}