{
  "annotation_id": "4ec4a6b5-d839-41cd-9717-ebab80cbeb34",
  "date_created": "2026-03-02T18:02:10.184000Z",
  "date_modified": "2026-03-02T18:02:10.184000Z",
  "file_hash": "281b4a6d7389f3e5a2d0db6d238f5dbc92488f2fa268bea5b280c16af0a94d23",
  "private": false,
  "record": {
    "abstract": "We examine the possible states of subsystems of a system of bits or qubits.\nIn the classical case (bits), this means the possible marginal distributions of\na probability distribution on a finite number of binary variables; we give\nnecessary and sufficient conditions for a set of probability distributions on\nall proper subsets of the variables to be the marginals of a single\ndistribution on the full set. In the quantum case (qubits), we consider mixed\nstates of subsets of a set of qubits; in the case of three qubits, we find\nquantum Bell inequalities -- necessary conditions for a set of two-qubit states\nto be the reduced states of a single mixed state of three qubits. We conjecture\nthat these conditions are also sufficient.",
    "arxiv_id": "quant-ph/0407227",
    "authors": [
      "Paul Butterley",
      "Anthony Sudbery",
      "Jason Szulc"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10701-005-9006-z",
    "journal_ref": "Found. Phys. 36, 83-101 (2006)",
    "title": "Compatibility of subsystem states",
    "url": "https://arxiv.org/abs/quant-ph/0407227"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b2cea915-2f17-4d86-9785-0a0f94cdfa3a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}