{
  "annotation_id": "a48dab90-517e-40c7-b094-df8f6ceb316d",
  "date_created": "2026-03-02T18:02:34.732000Z",
  "date_modified": "2026-03-02T18:02:34.732000Z",
  "file_hash": "68efad708b0734276ce8cd9ee2b74d2c58fbbf192c95bfd1886218af529e8c30",
  "private": false,
  "record": {
    "abstract": "We consider the pooling of quantum states when Alice and Bob both have one\npart of a tripartite system and, on the basis of measurements on their\nrespective parts, each infers a quantum state for the third part S. We denote\nthe conditioned states which Alice and Bob assign to S by alpha and beta\nrespectively, while the unconditioned state of S is rho. The state assigned by\nan overseer, who has all the data available to Alice and Bob, is omega. The\npooler is told only alpha, beta, and rho. We show that for certain classes of\ntripartite states, this information is enough for her to reconstruct omega by\nthe formula omega \\propto alpha rho^{-1} beta. Specifically, we identify two\nclasses of states for which this pooling formula works: (i) all pure states for\nwhich the rank of rho is equal to the product of the ranks of the states of\nAlice\u0027s and Bob\u0027s subsystems; (ii) all mixtures of tripartite product states\nthat are mutually orthogonal on S.",
    "arxiv_id": "quant-ph/0612190",
    "authors": [
      "Robert W. Spekkens",
      "H. M. Wiseman"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.75.042104",
    "journal_ref": "Phys. Rev. A 75, 042104 (2007)",
    "title": "Pooling quantum states obtained by indirect measurements",
    "url": "https://arxiv.org/abs/quant-ph/0612190"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6e76ca74-b1f2-4e5a-8182-cc055c671577",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}