{
  "id": "2211.02199",
  "version": "v1",
  "published": "2022-11-04T00:46:19.000Z",
  "updated": "2022-11-04T00:46:19.000Z",
  "title": "Characterization of the non-classical relation between measurement outcomes represented by non-orthogonal quantum states",
  "authors": [
    "Ming Ji",
    "Holger F. Hofmann"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Quantum mechanics describes seemingly paradoxical relations between the outcomes of measurements that cannot be performed jointly. In Hilbert space, the outcomes of such incompatible measurements are represented by non-orthogonal states. In this paper, we investigate how the relation between outcomes represented by non-orthogonal quantum states differs from the relations suggested by a joint assignment of measurement outcomes that do not depend on the actual measurement context. The analysis is based on a well-known scenario where three statements about the impossibilities of certain outcomes would seem to make a specific fourth outcome impossible as well, yet quantum theory allows the observation of that outcome with a non-vanishing probability. We show that the Hilbert space formalism modifies the relation between the four measurement outcomes by defining a lower bound of the fourth probability that increases as the total probability of the first three outcomes drops to zero. Quantum theory thus makes the violation of non-contextual consistency between the measurement outcomes not only possible, but actually requires it as a necessary consequence of the Hilbert space inner products that describe the contextual relation between the outcomes of different measurements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-04T00:46:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "measurement outcomes",
      "non-classical relation",
      "hilbert space formalism modifies",
      "characterization",
      "non-orthogonal quantum states differs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}