{
  "id": "2104.14996",
  "version": "v1",
  "published": "2021-04-30T13:28:43.000Z",
  "updated": "2021-04-30T13:28:43.000Z",
  "title": "In Wigner phase space, convolution explains why the vacuum majorizes mixtures of Fock states",
  "authors": [
    "Luc Vanbever"
  ],
  "comment": "16 pages, 1 figure",
  "categories": [
    "quant-ph"
  ],
  "abstract": "I show that the Wigner function that represents any mixture of the first 300 Fock states is majorized by the Wigner function of the vacuum state. As a consequence, the integration of any concave function over the Wigner phase space has a lower value for the vacuum state than for a mixture of Fock states. The Shannon differential entropy is an example of such concave function of significant physical importance. I demonstrate that the very cause of the majorization lies in the fact that a Wigner function is the result of a convolution. My proof is based on a new majorization result dedicated to the convolution of the negative exponential distribution with a precisely constrained function. I present a geometrical interpretation of the new majorization property in a discrete setting and extend this relation to a continuous setting. The final part of my proof is numerical and consolidates my previous findings: remarkably, I find that the first 300 Fock states match the entry criteria of my new majorization result - with strong indications that it applies to any Fock state.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-30T13:28:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fock state",
      "wigner phase space",
      "vacuum majorizes mixtures",
      "convolution explains",
      "wigner function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}