{
  "annotation_id": "bd50528c-9291-46f9-bec4-004851af9627",
  "date_created": "2026-03-02T18:02:27.616000Z",
  "date_modified": "2026-03-02T18:02:27.616000Z",
  "file_hash": "cd56bbd8ed0f4de346bbbfea4be7d6e226f3c32a0788ee51eaa8075997e35e85",
  "private": false,
  "record": {
    "abstract": "We report on an \"anti-Gleason\" phenomenon in classical mechanics: in contrast\nwith the quantum case, the algebra of classical observables can carry a\nnon-linear quasi-state, a monotone functional which is linear on all subspaces\ngenerated by Poisson-commutative functions. We present an example of such a\nquasi-state in the case when the phase space is the 2-sphere. This example lies\nin the intersection of two seemingly remote mathematical theories - symplectic\ntopology and the theory of topological quasi-states. We use this quasi-state to\nestimate the error of the simultaneous measurement of non-commuting\nHamiltonians.",
    "arxiv_id": "quant-ph/0606214",
    "authors": [
      "Michael Entov",
      "Leonid Polterovich",
      "Frol Zapolsky"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10701-007-9158-0",
    "title": "An \"anti-Gleason\" phenomenon and simultaneous measurements in classical   mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0606214"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8ff77ef4-ae60-44f2-bb07-b801854e11e0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}