{
  "annotation_id": "edfcb462-58d7-4255-96bf-73a7db67c2ab",
  "date_created": "2026-03-02T18:02:06.880000Z",
  "date_modified": "2026-03-02T18:02:06.880000Z",
  "file_hash": "7aa077c26accbf78ae1e13d8dd042573ec8df7f67a36083e0c57b6664c54a4cc",
  "private": false,
  "record": {
    "abstract": "A test space is the set of outcome-sets associated with a collection of\nexperiments. This notion provides a simple mathematical framework for the study\nof probabilistic theories -- notably, quantum mechanics -- in which one is\nfaced with incommensurable random quantities. In the case of quantum mechanics,\nthe relevant test space, the set of orthonormal bases of a Hilbert space,\ncarries significant topological structure. This paper inaugurates a general\nstudy of topological test spaces. Among other things, we show that any\ntopological test space with a compact space of outcomes is of finite rank. We\nalso generalize results of Meyer and Clifton-Kent by showing that, under very\nweak assumptions, any second-countable topological test space contains a dense\nsemi-classical test space.",
    "arxiv_id": "quant-ph/0405178",
    "authors": [
      "Alexander Wilce"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10773-005-4682-1",
    "title": "Topological Test Spaces",
    "url": "https://arxiv.org/abs/quant-ph/0405178"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "41262cac-227f-4ed1-842e-22d216ff4a70",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}