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THE SET OF QUANTUM CORRELATIONS IS NOT CLOSED
Forum of Mathematics, Pi ( IF 2.955 ) Pub Date : 2019-01-14 , DOI: 10.1017/fmp.2018.3
WILLIAM SLOFSTRA

We construct a linear system nonlocal 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 nonlocal 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 finite-dimensional strategy, or a limit of finite-dimensional quantum strategies.

中文翻译:

量子相关性的集合不是封闭的

我们构建了一个线性系统非局部博弈,它可以使用有限维量子策略的限制完美地玩,但不能在任何有限维希尔伯特空间上完美地玩,甚至不能使用任何张量积策略。特别是,这表明(张量积)量子相关性的集合不是封闭的。构造的非局部博弈为“中间”Tsirelson 问题提供了另一个反例,其证明比我们之前的论文更短(尽管失去了通用嵌入定理)。我们还表明,确定线性系统博弈是否可以用有限维策略或有限维量子策略的限制完美地玩是不确定的。
更新日期:2019-01-14
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