{
  "annotation_id": "95ea9192-74fb-4f44-8d3c-e92f89a31abe",
  "date_created": "2026-03-02T18:02:03.319000Z",
  "date_modified": "2026-03-02T18:02:03.319000Z",
  "file_hash": "340d5e15c5ed05af2d11822a0874ab535568a10786f4e1fe580025013516c181",
  "private": false,
  "record": {
    "abstract": "When the state of a quantum system belongs to a N-dimensional Hilbert space,\nwith N the power of a prime number, it is possible to associate to the system a\nfinite field (Galois field) with N elements. In this paper, we introduce\ngeneralized Bell states that can be intrinsically expressed in terms of the\nfield operations.These Bell states are in one to one correspondence with the\nN^2 elements of the generalised Pauli group or Heisenberg-Weyl group.\n  This group consists of discrete displacement operators and provides a\ndiscrete realisation of the Weyl function.Thanks to the properties of\ngeneralised Bell states and of quadratic extensions of finite fields, we derive\na particular solution for the Mean King\u0027s problem. This solution is in turn\nshown to be in one to one correspondence with a set of N^2 self-adjoint\noperators that provides a discrete realisation of the Wigner\nquasi-distribution.",
    "arxiv_id": "quant-ph/0401037",
    "authors": [
      "Thomas Durt"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Bell states, mutually unbiased bases and the Mean King\u0027s problem",
    "url": "https://arxiv.org/abs/quant-ph/0401037"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3baf82f7-0434-434b-85b0-67ad37c1452a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}