{
  "annotation_id": "b7c19d23-a2be-46f1-8faf-e4b44656318e",
  "date_created": "2026-03-02T18:02:09.997000Z",
  "date_modified": "2026-03-02T18:02:09.997000Z",
  "file_hash": "4837f2b1020e2263e60bb31f802a5a61d027d4e5756aa81489faad43dc1e414c",
  "private": false,
  "record": {
    "abstract": "This paper initiates the study of hidden variables from the discrete,\nabstract perspective of quantum computing. For us, a hidden-variable theory is\nsimply a way to convert a unitary matrix that maps one quantum state to\nanother, into a stochastic matrix that maps the initial probability\ndistribution to the final one in some fixed basis. We list seven axioms that we\nmight want such a theory to satisfy, and then investigate which of the axioms\ncan be satisfied simultaneously. Toward this end, we construct a new\nhidden-variable theory that is both robust to small perturbations and\nindifferent to the identity operation, by exploiting an unexpected connection\nbetween unitary matrices and network flows. We also analyze previous\nhidden-variable theories of Dieks and Schrodinger in terms of our axioms. In a\ncompanion paper, we will show that actually sampling the history of a hidden\nvariable under reasonable axioms is at least as hard as solving the Graph\nIsomorphism problem; and indeed is probably intractable even for quantum\ncomputers.",
    "arxiv_id": "quant-ph/0408035",
    "authors": [
      "Scott Aaronson"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.71.032325",
    "title": "Quantum Computing and Hidden Variables I: Mapping Unitary to Stochastic   Matrices",
    "url": "https://arxiv.org/abs/quant-ph/0408035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ea8669fd-643d-447a-8256-8d803f5d888d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}