{
  "annotation_id": "720cfc12-c3a8-4d91-8550-00c57f3263e1",
  "date_created": "2026-03-02T18:02:34.416000Z",
  "date_modified": "2026-03-02T18:02:34.416000Z",
  "file_hash": "ce6e91bf913498ad0e74aa911163d23c9c62010d7055cb0850bcf6250daece49",
  "private": false,
  "record": {
    "abstract": "We show that any quantum density matrix can be represented by a Bayesian\nnetwork (a directed acyclic graph), and also by a Markov network (an undirected\ngraph). We show that any Bayesian or Markov net that represents a density\nmatrix, is logically equivalent to a set of conditional independencies\n(symmetries) satisfied by the density matrix. We show that the d-separation\ntheorems of classical Bayesian and Markov networks generalize in a simple and\nnatural way to quantum physics. The quantum d-separation theorems are shown to\nbe closely connected to quantum entanglement. We show that the graphical rules\nfor d-separation can be used to detect pairs of nodes (or of node sets) in a\ngraph that are unentangled. CMI entanglement (a.k.a. squashed entanglement), a\nmeasure of entanglement originally discovered by analyzing Bayesian networks,\nis an important part of the theory of this paper.",
    "arxiv_id": "quant-ph/0701201",
    "authors": [
      "Robert R. Tucci"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Factorization of Quantum Density Matrices According to Bayesian and   Markov Networks",
    "url": "https://arxiv.org/abs/quant-ph/0701201"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5d869dd8-78c8-4d88-a190-d1d2a8c488b2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}