{
  "id": "quant-ph/0407043",
  "version": "v2",
  "published": "2004-07-06T10:56:39.000Z",
  "updated": "2004-07-15T17:23:46.000Z",
  "title": "Path summation and quantum measurements",
  "authors": [
    "D. Sokolovski",
    "R. Sala Mayato"
  ],
  "comment": "30 pages+3 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We propose a general theoretical approach to quantum measurements based on the path (histories) summation technique. For a given dynamical variable A, the Schr\\\"odinger state of a system in a Hilbert space of arbitrary dimensionality is decomposed into a set of substates, each of which corresponds to a particular detailed history of the system. The coherence between the substates may then be destroyed by meter(s) to a degree determined by the nature and the accuracy of the measurement(s) which may be of von Neumann, finite-time or continuous type. Transformations between the histories obtained for non-commuting variables and construction of simultaneous histories for non-commuting observables are discussed. Important cases of a particle described by Feynman paths in the coordinate space and a qubit in a two dimensional Hilbert space are studied in some detail.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-07-15T17:23:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum measurements",
      "path summation",
      "dimensional hilbert space",
      "general theoretical approach",
      "summation technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004quant.ph..7043S"
    }
  }
}