{
  "id": "2506.14693",
  "version": "v2",
  "published": "2025-06-17T16:32:29.000Z",
  "updated": "2025-06-21T13:14:29.000Z",
  "title": "Einstein causality of quantum measurements in the Tomonaga-Schwinger picture",
  "authors": [
    "Samuel Fedida"
  ],
  "comment": "18 pages, 5 figures",
  "categories": [
    "quant-ph",
    "gr-qc",
    "hep-th"
  ],
  "abstract": "When quantum measurements are conducted over spacelike-separated regions of spacetime, a natural and commonly assumed physical postulate, called Einstein causality, asserts that they should commute. In this paper, we provide a generalisation to L\\\"uders' rule \\`a la Aharonov-Albert in those globally hyperbolic spacetimes which allow unitarily equivalent Hilbert spaces to be defined along Cauchy hypersurfaces, thus relying on the existence of an interaction picture \\`a la Tomonaga-Schwinger. We show that under this rule, selective quantum measurements satisfy a state-independent anyonic commutation relation over spacelike-separated (pre)compact regions. We highlight that this propagates to positive operator-valued measures (POVMs), where the commutation is necessarily bosonic. In the simplistic scenario where the measurements are assumed to be instantaneous, this implies quantum no-signalling for non-selective measurements. We then examine Sorkin's impossible measurements and show that immediate contradictions can be averted as long as collapse-inducing measurements are irreversible. We finish by discussing the possibility of extending such results beyond the interaction picture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-06-21T13:14:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "einstein causality",
      "tomonaga-schwinger picture",
      "state-independent anyonic commutation relation",
      "interaction picture",
      "unitarily equivalent hilbert spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}