{
  "annotation_id": "5b7bb687-c557-4936-a64c-01e3a514b74b",
  "date_created": "2026-03-02T18:02:12.979000Z",
  "date_modified": "2026-03-02T18:02:12.979000Z",
  "file_hash": "632f5b9a4ab58baf57fae4c69861d846be06fe20519199b76e2d1453b863003f",
  "private": false,
  "record": {
    "abstract": "We show that for two classical brownian particles there exists an analog of\ncontinuous-variable quantum entanglement: The common probability distribution\nof the two coordinates and the corresponding coarse-grained velocities cannot\nbe prepared via mixing of any factorized distributions referring to the two\nparticles in separate. This is possible for particles which interacted in the\npast, but do not interact in the present. Three factors are crucial for the\neffect: 1) separation of time-scales of coordinate and momentum which motivates\nthe definition of coarse-grained velocities; 2) the resulting uncertainty\nrelations between the coordinate of the brownian particle and the change of its\ncoarse-grained velocity; 3) the fact that the coarse-grained velocity, though\npertaining to a single brownian particle, is defined on a common context of two\nparticles. The brownian entanglement is a consequence of a coarse-grained\ndescription and disappears for a finer resolution of the brownian motion. We\ndiscuss possibilities of its experimental realizations in examples of\nmacroscopic brownian motion.",
    "arxiv_id": "quant-ph/0412132",
    "authors": [
      "A. E. Allahverdyan",
      "A. Khrennikov",
      "Th. M. Nieuwenhuizen"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.stat-mech"
    ],
    "doi": "10.1103/PhysRevA.72.032102",
    "title": "Brownian Entanglement",
    "url": "https://arxiv.org/abs/quant-ph/0412132"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3b4cc50c-f634-4f57-9ecd-c6df327a6e5a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}