{
  "annotation_id": "add0391f-90ec-44c7-accc-b4bbff942673",
  "date_created": "2026-03-02T18:01:53.155000Z",
  "date_modified": "2026-03-02T18:01:53.155000Z",
  "file_hash": "232a5e53f2980ff39599d5359416eeb208819d921d9e614f46098cb95a0bba64",
  "private": false,
  "record": {
    "abstract": "Given a uniform ensemble of quantum density matrices $\\rho$, it is useful to\ncalculate the mean value over this ensemble of a product of entries of $\\rho$.\nWe show how to calculate such moments in this paper. The answer involves well\nknown results from Group Representation Theory and Random Matrix Theory. This\nquantum problem has a well known classical counterpart: given a uniform\nensemble of probability distributions $P=(P_1, P_2, ..., P_N)$ where the $P_j$\nare non-negative reals that sum to one, calculate the mean value over this\nprobability simplex of products of $P$ components. The answer to the classical\nproblem follows from an integral formula due to Dirichlet.",
    "arxiv_id": "quant-ph/0206193",
    "authors": [
      "Robert R. Tucci"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "All Moments of the Uniform Ensemble of Quantum Density Matrices",
    "url": "https://arxiv.org/abs/quant-ph/0206193"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4b2a2d2e-7c32-4260-8129-38d3d47b9542",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}