{
  "id": "1703.08618",
  "version": "v1",
  "published": "2017-03-24T22:44:51.000Z",
  "updated": "2017-03-24T22:44:51.000Z",
  "title": "The set of quantum correlations is not closed",
  "authors": [
    "William Slofstra"
  ],
  "comment": "28 pages",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.GR",
    "math.MP",
    "math.OA"
  ],
  "abstract": "We construct a linear system non-local game which can be played perfectly using a limit of finite-dimensional quantum strategies, but which cannot be played perfectly on any finite-dimensional Hilbert space, or even with any tensor-product strategy. In particular, this shows that the set of (tensor-product) quantum correlations is not closed. The constructed non-local game provides another counterexample to the \"middle\" Tsirelson problem, with a shorter proof than our previous paper (though at the loss of the universal embedding theorem). We also show that it is undecidable to determine if a linear system game can be played perfectly with a limit of finite-dimensional quantum strategies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-24T22:44:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum correlations",
      "finite-dimensional quantum strategies",
      "linear system non-local game",
      "finite-dimensional hilbert space",
      "linear system game"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}