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.

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Tsirelson 问题和非局部博弈产生的群的嵌入定理

Tsirelson 的问题询问二方量子相关的交换算子模型是否等价于张量积模型。我们通过证明存在具有完美通勤算子策略但不具有完美张量积策略的非本地博弈来给出否定的答案。已知等价于 Connes 嵌入问题的弱 Tsirelson 问题仍然开放。我们构建的示例是（二元）线性系统游戏的实例。对于此类博弈，先前的结果表明完美策略的存在是由线性系统的解组控制的。我们的主要结果是每个有限呈现的群都嵌入到某个解群中。作为一个额外的后果，