{
  "id": "2104.03661",
  "version": "v1",
  "published": "2021-04-08T10:22:38.000Z",
  "updated": "2021-04-08T10:22:38.000Z",
  "title": "Uncertainty relation between detection probability and energy fluctuations",
  "authors": [
    "Felix Thiel",
    "Itay Mualem",
    "David Kessler",
    "Eli Barkai"
  ],
  "comment": "12 pages, special issue Axiomatic Approaches to Quantum Mechanics, 4 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it is fully exploring space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-08T10:22:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "detection probability",
      "energy fluctuations",
      "uncertainty relation",
      "induce effectively non-ergodic features",
      "classical random walker"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}