{
  "annotation_id": "83f17b3a-de51-408a-addb-50ae83f493a6",
  "date_created": "2026-03-02T18:01:52.223000Z",
  "date_modified": "2026-03-02T18:01:52.223000Z",
  "file_hash": "00356651a744ca1dd342ada948f6ae9b6061653b589d569e3fbd85b399780737",
  "private": false,
  "record": {
    "abstract": "We illustrate some problems that are related to the existence of an\nunderlying linear structure at the level of the property lattice associated\nwith a physical system, for the particular case of two explicitly separated\nspin 1/2 objects that are considered, and mathematically described, as one\ncompound system. It is shown that the separated product of the property\nlattices corresponding with the two spin 1/2 objects does not have an\nunderlying linear structure, although the property lattices associated with the\nsubobjects in isolation manifestly do. This is related at a fundamental level\nto the fact that separated products do not behave well with respect to the\ncovering law (and orthomodularity) of elementary lattice theory. In addition,\nwe discuss the orthogonality relation associated with the separated product in\ngeneral and consider the related problem of the behavior of the corresponding\nSasaki projections as partial state space mappings",
    "arxiv_id": "quant-ph/0205166",
    "authors": [
      "Diederik Aerts",
      "Frank Valckenborgh"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/9789812778024_0003",
    "title": "Linearity and Compound Physical Systems: The Case of Two Separated Spin   1/2 Entities",
    "url": "https://arxiv.org/abs/quant-ph/0205166"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "853c7919-b5f7-40fb-b2be-d155d1fb6a9e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}