{
  "id": "1612.07023",
  "version": "v1",
  "published": "2016-12-21T09:25:35.000Z",
  "updated": "2016-12-21T09:25:35.000Z",
  "title": "Geometric approach to modular and weak values of discrete quantum systems",
  "authors": [
    "Mirko Cormann",
    "Yves Caudano"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "We express modular and weak values of three- and high-level quantum systems in their polar form. Within the Majorana representation and a purely geometric approach, we point out that this complex values of N-level quantum systems possess a modulus determined by the product of N-1 square roots of probability ratios and an argument deduced from a sum of N-1 spherical polygons on the Bloch sphere. This theoretical results demonstrate that the discontinuous effects around singularities of weak values have a purely geometric origin with no classical counterpart. Furthermore, the geometric approach is used to extend the three-box paradox [1] to a larger class of quantum phenomena: quantum entanglement. Therefore, we present a two spin-1/2 measurement experiment, for which Alice and Bob come to counter-intuitive conclusions about the particles' state between pre- and postselection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-21T09:25:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak values",
      "discrete quantum systems",
      "n-level quantum systems possess",
      "high-level quantum systems",
      "purely geometric approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}