{
  "id": "0905.3810",
  "version": "v1",
  "published": "2009-05-23T11:51:43.000Z",
  "updated": "2009-05-23T11:51:43.000Z",
  "title": "Weak values, 'negative probability' and the uncertainty principle",
  "authors": [
    "D. Sokolovski"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "A quantum transition can be seen as a result of interference between various pathways(e.g. Feynman paths) which can be labelled by a variable $f$. An attempt to determine the value of f without destroying the coherence between the pathways produces a weak value of $\\bar{f}$. We show $\\bar{f}$ to be an average obtained with amplitude distribution which can, in general, take negative values which, in accordance with the uncertainty principle, need not contain information about the actual range of the values $f$ which contribute to the transition. It is also demonstrated that the moments of such alternating distributions have a number of unusual properties which may lead to misinterpretation of the weak measurement results.We provide a detailed analysis of weak measurements with and without post-selection. Examples include the double slit diffraction experiment,weak von Neumann and von Neumann-like measurements, traversal time for an elastic collision, the phase time, the local angular momentum(LAM) and the 'three-box case' of {\\it Aharonov et al}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-23T11:51:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uncertainty principle",
      "weak value",
      "negative probability",
      "weak measurement results",
      "double slit diffraction experiment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.3810S"
    }
  }
}