{
  "annotation_id": "e37c4a1d-f2fe-43cb-b802-73fce00cf82a",
  "date_created": "2026-03-02T18:01:59.065000Z",
  "date_modified": "2026-03-02T18:01:59.065000Z",
  "file_hash": "c7a58759944997e22f7e38450128ba831100cae65e97d6a2292508eef847ef34",
  "private": false,
  "record": {
    "abstract": "We prove a Gleason-type theorem for the quantum probability rule using frame\nfunctions defined on positive-operator-valued measures (POVMs), as opposed to\nthe restricted class of orthogonal projection-valued measures used in the\noriginal theorem. The advantage of this method is that it works for\ntwo-dimensional quantum systems (qubits) and even for vector spaces over\nrational fields--settings where the standard theorem fails. Furthermore, unlike\nthe method necessary for proving the original result, the present one is rather\nelementary. In the case of a qubit, we investigate similar results for frame\nfunctions defined upon various restricted classes of POVMs. For the so-called\ntrine measurements, the standard quantum probability rule is again recovered.",
    "arxiv_id": "quant-ph/0306179",
    "authors": [
      "Carlton M. Caves",
      "Christopher A. Fuchs",
      "Kiran Manne",
      "Joseph M. Renes"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1023/B:FOOP.0000019581.00318.a5",
    "journal_ref": "Found. Phys. 34, 193 (2004)",
    "title": "Gleason-Type Derivations of the Quantum Probability Rule for Generalized   Measurements",
    "url": "https://arxiv.org/abs/quant-ph/0306179"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2d9804e6-d6f2-49a2-a6e7-f133b9ac49dd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}