2016/06/30 by William Slofstra · 2 citations
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.GR #math.MP #math.OA
paper · pdf · doi:10.1090/jams/929
published as J. Amer. Math. Soc. 33 (2020), 1-56 · Update to match published version, including a new background section on quantum correlation sets, fixes to the definition of pictures in Section 6 (the previous definition using smooth curves allowed some pathological behaviour), and other minor changes throughout. 66 pages, 36 figures
arxiv created 2020/09/27 · arxiv updated 2020/09/29
Tsirelson's problem asks whether the commuting operator model for two-party quantum correlations is equivalent to the tensor-product model. We give a negative answer to this question by showing that there are non-local games which have perfect commuting-operator strategies, but do not have perfect tensor-product strategies. The weak Tsirelson problem, which is known to be equivalent to Connes embedding problem, remains open. The examples we construct are instances of (binary) linear system games. For such games, previous results state that the existence of perfect strategies is controlled by the solution group of the linear system. Our main result is that every finitely-presented group embeds in some solution group. As an additional consequence, we show that the problem of determining whether a linear system game has a perfect commuting-operator strategy is undecidable.