{
  "annotation_id": "4a96e5b6-bfb8-4dea-8154-9ccda234c992",
  "date_created": "2026-03-02T18:02:41.154000Z",
  "date_modified": "2026-03-02T18:02:41.154000Z",
  "file_hash": "ee5f44fdf645e0b9fc69130379f47e30ee0f4cef65deb2c22501c1341d30bf1b",
  "private": false,
  "record": {
    "abstract": "A general `quantum history theory\u0027 can be characterised by the space of\nhistories and by the space of decoherence functionals. In this note we consider\nthe situation where the space of histories is given by the lattice of\nprojection operators on an infinite dimensional Hilbert space $H$. We study\noperator representations for decoherence functionals on this space of\nhistories. We first give necessary and sufficient conditions for a decoherence\nfunctional being representable by a trace class operator on $H \\otimes H$, an\ninfinite dimensional analogue of the Isham-Linden-Schreckenberg representation\nfor finite dimensions. Since this excludes many decoherence functionals of\nphysical interest, we then identify the large and physically important class of\ndecoherence functionals which can be represented, canonically, by bounded\noperators on $H \\otimes H$.",
    "arxiv_id": "quant-ph/9706001",
    "authors": [
      "Oliver Rudolph",
      "J. D. Maitland Wright"
    ],
    "categories": [
      "quant-ph",
      "funct-an",
      "gr-qc",
      "math.FA"
    ],
    "doi": "10.1063/1.532157",
    "journal_ref": "J.Math.Phys. 38 (1997) 5643-5652",
    "title": "On Tracial Operator Representations of Quantum Decoherence Functionals",
    "url": "https://arxiv.org/abs/quant-ph/9706001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ae1c2dc9-12df-44e5-8001-2f1e3a192c8b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}