Tsirelson’s problem and an embedding theorem for groups arising from non-local games
Tsirelson’s problem and an embedding theorem for groups arising from non-local games
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DOI：
10.1090/jams/929
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发表时间：
2016-06
影响因子：
3.9
通讯作者：
William Slofstra
中科院分区：
文献类型：
--
作者：
William Slofstra
Tsirelson的问题是两方量子关联的交换算符模型是否等价于张量积模型。我们给出了一个否定的答案，这个问题表明，有非本地的游戏，有完美的张量算子的战略，但没有完美的张量积战略。弱Tsirelson问题，这是已知的是相当于康纳斯嵌入问题，仍然开放。我们构造的例子是（二进制）线性系统游戏的实例。对于这样的游戏，以前的结果表明，完美的策略的存在性是由线性系统的解群控制。我们的主要结果是每个有限呈现群嵌入到某个解群中。作为一个额外的后果，我们表明，问题的确定是否线性系统的游戏有一个完美的决策运营商的战略是不可判定的。
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 the 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.