{
  "annotation_id": "2463c3e8-1af0-45e2-8b91-01072f410755",
  "date_created": "2026-03-02T18:02:34.551000Z",
  "date_modified": "2026-03-02T18:02:34.551000Z",
  "file_hash": "1b65a2e8ef5ff2cda487efed17612e867c7bc1ecdcbba1cd9aa35bd9fc574309",
  "private": false,
  "record": {
    "abstract": "We present a framework, compliant with the general canonical principle of\nstatistical mechanics, to define measures on the set of pure Gaussian states of\ncontinuous variable systems. Within such a framework, we define two specific\nmeasures, referred to as `micro-canonical\u0027 and `canonical\u0027, and apply them to\nstudy systematically the statistical properties of the bipartite entanglement\nof n-mode pure Gaussian states (as quantified by the entropy of a subsystem).\nWe rigorously prove the \"concentration of measure\" around a finite average,\noccurring for the entanglement in the thermodynamical limit in both the\ncanonical and the micro-canonical approach. For finite n, we determine\nanalytically the average and standard deviation of the entanglement (as\nquantified by the reduced purity) between one mode and all the other modes.\nFurthermore, we numerically investigate more general situations, clearly\nshowing that the onset of the concentration of measure already occurs at\nrelatively small n.",
    "arxiv_id": "quant-ph/0701051",
    "authors": [
      "A. Serafini",
      "O. C. O. Dahlsten",
      "D. Gross",
      "M. B. Plenio"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/1751-8113/40/31/027",
    "journal_ref": "J. Phys. A: Math. Theor. 40, 9551 (2007)",
    "title": "Canonical and micro-canonical typical entanglement of continuous   variable systems",
    "url": "https://arxiv.org/abs/quant-ph/0701051"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ab616b44-9c2b-493e-ae19-b2f7cb610f6d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}