{
  "id": "1410.2732",
  "version": "v1",
  "published": "2014-10-10T10:36:05.000Z",
  "updated": "2014-10-10T10:36:05.000Z",
  "title": "Local numerical range for a class of $2\\otimes d$ hermitian operators",
  "authors": [
    "J. Jurkowski",
    "A. Rutkowski",
    "D. Chruściński"
  ],
  "journal": "Open Systems & Information Dynamics 17 (04), 347-359, 2010",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A local numerical range is analyzed for a family of circulant observables and states of composite $2 \\otimes d$ systems. It is shown that for any $2\\otimes d$ circulant operator $\\cal O$ there exists a basis giving rise to the matrix representation with real non-negative off-diagonal elements. In this basis the problem of finding extremum of $\\cal O$ on product vectors $\\ket{x}\\otimes \\ket{y} \\in \\mathbb{C}^2\\otimes \\mathbb{C}^d$ reduces to the corresponding problem in $\\mathbb{R}^2\\otimes \\mathbb{R}^d$. The final analytical result for $d=2$ is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-10T10:36:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local numerical range",
      "hermitian operators",
      "real non-negative off-diagonal elements",
      "final analytical result",
      "product vectors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.2732J"
    }
  }
}