{
  "id": "2002.00004",
  "version": "v1",
  "published": "2020-01-31T12:33:04.000Z",
  "updated": "2020-01-31T12:33:04.000Z",
  "title": "Optimal upper bound of entropic uncertainty relation for mutually unbiased bases",
  "authors": [
    "Bilal Canturk",
    "Zafer Gedik"
  ],
  "comment": "10 pages, no figures, regular article. We had submitted this manuscript to Physical Review A. We took a revision request. This manuscript is the revised version",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We have obtained the optimal upper bound of entropic uncertainty relation for $N$ Mutually Unbiased Bases (MUBs). We have used the methods of variational calculus for the states that can be written in terms of $N$ MUBs. Our result is valid for any state when $N$ is $d+1$, where $d$ is the dimension of the related system. We have pointed out the fact that our result provides a quantitative criterion for the extendable of MUBs. In addition, we have applied our result to the mutual information of $d+1$ observables conditioned with a classical memory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-31T12:33:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entropic uncertainty relation",
      "optimal upper bound",
      "mutually unbiased bases",
      "variational calculus",
      "mutual information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}