{
  "annotation_id": "eb034cd6-2531-4649-9881-a2239260df0d",
  "date_created": "2026-03-02T18:02:34.485000Z",
  "date_modified": "2026-03-02T18:02:34.485000Z",
  "file_hash": "52ae1486f1aeddb85ab1120423e9fb4500912421459a5945600b3b0e48a97d4c",
  "private": false,
  "record": {
    "abstract": "The mean king problem is a quantum mechanical retrodiction problem, in which\nAlice has to name the outcome of an ideal measurement on a d-dimensional\nquantum system, made in one of (d+1) orthonormal bases, unknown to Alice at the\ntime of the measurement. Alice has to make this retrodiction on the basis of\nthe classical outcomes of a suitable control measurement including an entangled\ncopy. We show that the existence of a strategy for Alice is equivalent to the\nexistence of an overall joint probability distribution for (d+1) random\nvariables, whose marginal pair distributions are fixed as the transition\nprobability matrices of the given bases. In particular, for d=2 the problem is\ndecided by John Bell\u0027s classic inequality for three dichotomic variables. For\nmutually unbiased bases in any dimension Alice has a strategy, but for randomly\nchosen bases the probability for that goes rapidly to zero with increasing d.",
    "arxiv_id": "quant-ph/0612035",
    "authors": [
      "M. Reimpell",
      "R. F. Werner"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.75.062334",
    "journal_ref": "Phys. Rev. A 75, 062334 (2007)",
    "title": "A Meaner King uses Biased Bases",
    "url": "https://arxiv.org/abs/quant-ph/0612035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5ccee4e9-0d75-4f6e-b829-a7c0a6b8fcc1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}