{
  "id": "2106.11334",
  "version": "v1",
  "published": "2021-06-21T18:03:26.000Z",
  "updated": "2021-06-21T18:03:26.000Z",
  "title": "Hierarchy of continuous-variable quantum resource theories",
  "authors": [
    "Giulio Gianfelici",
    "Hermann Kampermann",
    "Dagmar Bruß"
  ],
  "comment": "22 pages, 3 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Connections between the resource theories of coherence and purity (or non-uniformity) are well known for discrete-variable, finite-dimensional, quantum systems. We establish analogous results for continuous-variable systems, in particular Gaussian systems. To this end, we define the concept of maximal coherence at fixed energy, which is achievable with energy-preserving unitaries. We show that the maximal Gaussian coherence (where states and operations are required to be Gaussian) can be quantified analytically by the relative entropy. We then propose a resource theory of non-uniformity, by considering the purity of a quantum state at fixed energy as resource, and by defining non-uniformity monotones. In the Gaussian case, we prove the equality of Gaussian non-uniformity and maximal Gaussian coherence. Finally, we show a hierarchy for non-uniformity, coherence, discord and entanglement in continuous-variable systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-21T18:03:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "resource theory",
      "continuous-variable quantum resource theories",
      "maximal gaussian coherence",
      "non-uniformity",
      "continuous-variable systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}