{
  "annotation_id": "9426eb8b-a9f9-4de8-90e2-a481c36cd593",
  "date_created": "2026-03-02T18:01:59.540000Z",
  "date_modified": "2026-03-02T18:01:59.540000Z",
  "file_hash": "a368b5907cf93c905178e3cc5c3cfc96cd700babd890e2a6616b0366aab96181",
  "private": false,
  "record": {
    "abstract": "Gaussian states -- or, more generally, Gaussian operators -- play an\nimportant role in Quantum Optics and Quantum Information Science, both in\ndiscussions about conceptual issues and in practical applications. We describe,\nin a tutorial manner, a systematic operator method for first characterizing\nsuch states and then investigating their properties. The central numerical\nquantities are the covariance matrix that specifies the characteristic function\nof the state, and the closely related matrices associated with Wigner\u0027s and\nGlauber\u0027s phase space functions. For pedagogical reasons, we restrict the\ndiscussion to one-dimensional and two-dimensional Gaussian states, for which we\nprovide illustrating and instructive examples.",
    "arxiv_id": "quant-ph/0307196",
    "authors": [
      "Berthold-Georg Englert",
      "Krzysztof W\u00f3dkiewicz"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "International Journal of Quantum Information, Vol. 1, No. 2 (2003)\n  153-188",
    "title": "Tutorial Notes on One-Party and Two-Party Gaussian States",
    "url": "https://arxiv.org/abs/quant-ph/0307196"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8d2f4dd1-8853-498e-ac84-fc28f5f77df7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}