{
  "annotation_id": "32dd4677-15e8-44a4-97f6-07d8d2398a3d",
  "date_created": "2026-03-02T18:02:03.605000Z",
  "date_modified": "2026-03-02T18:02:03.605000Z",
  "file_hash": "7191b48a605d3ac90bec217ba61b9f9a575a326b5e651cf66da02b5b5818d749",
  "private": false,
  "record": {
    "abstract": "In a quantum system having a finite number $N$ of orthogonal states, two\northonormal bases $\\{a_i\\}$ and $\\{b_j\\}$ are called mutually unbiased if all\ninner products $\u003ca_i|b_j\u003e$ have the same modulus $1/\\sqrt{N}$. This concept\nappears in several quantum information problems. The number of pairwise\nmutually unbiased bases is at most $N+1$ and various constructions of $N+1$\nsuch bases have been found when $N$ is a power of a prime number. We study\nfamilies of formulas that generalize these constructions to arbitrary\ndimensions using finite rings.We then prove that there exists a set of $N+1$\nmutually unbiased bases described by such formulas, if and only if $N$ is a\npower of a prime number.",
    "arxiv_id": "quant-ph/0312204",
    "authors": [
      "Claude archer"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "There is no generalization of known formulas for mutually unbiased bases",
    "url": "https://arxiv.org/abs/quant-ph/0312204"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "33cd9a6a-3944-4c3a-9b56-2d1cbe0f548f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}