{
  "id": "1704.06516",
  "version": "v1",
  "published": "2017-04-21T12:59:59.000Z",
  "updated": "2017-04-21T12:59:59.000Z",
  "title": "A sufficient condition for non-existence of symmetric extension of qudits using Bell inequalities",
  "authors": [
    "Meenu Kumari",
    "Shohini Ghose",
    "Robert B. Mann"
  ],
  "comment": "6 pages, 3 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We analyze the connection between Bell inequality violations and symmetric extendibility of quantum states. We prove that 2-qubit reduced states of multiqubit symmetric pure states do not violate the Bell-CHSH inequality. We then prove the more general converse that any 2-qubit state that violates the CHSH inequality cannot have a symmetric extension. We extend our analysis to qudits and provide a test for symmetric extendibility of 2-qudit states. We show that if a 2-qudit Bell inequality is monogamous, then any 2-qudit state that violates this inequality does not have a symmetric extension. For the specific case of 2-qutrit states, we use numerical evidence to conjecture that the CGLMP inequality is monogamous. Hence, the violation of the CGLMP inequality by any 2-qutrit state could be a sufficient condition for the non-existence of its symmetric extension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-21T12:59:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric extension",
      "sufficient condition",
      "non-existence",
      "symmetric extendibility",
      "multiqubit symmetric pure states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}