A synchronous game for binary constraint systems
A synchronous game for binary constraint systems
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DOI：
10.1063/1.4996867
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发表时间：
2017-07
期刊：
影响因子：
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通讯作者：
Se-Jin Kim;V. Paulsen;Christopher Schafhauser
中科院分区：
文献类型：
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作者：
Se-Jin Kim;V. Paulsen;Christopher Schafhauser
最近，W.Slofstra证明了量子关联集不是封闭的。通过给出一个具有完美量子近似策略但没有完美量子策略的同步博弈的例子，我们证明了同步量子关联集不是封闭的，这意味着他的结果。我们还展示了一个图，其量子独立数和量子近似独立数是不同的。我们证明了同步量子近似关联和同步量子空间关联的新特征。我们解决了Dykema和第二作者的同步逼近问题，得到了Connes嵌入问题在同步关联方面的一个新的等价性。
Recently, W. Slofstra proved that the set of quantum correlations is not closed. We prove that the set of synchronous quantum correlations is not closed, which implies his result, by giving an example of a synchronous game that has a perfect quantum approximate strategy but no perfect quantum strategy. We also exhibit a graph for which the quantum independence number and the quantum approximate independence number are different. We prove new characterisations of synchronous quantum approximate correlations and synchronous quantum spatial correlations. We solve the synchronous approximation problem of Dykema and the second author, which yields a new equivalence of Connes' embedding problem in terms of synchronous correlations.