In this paper, we construct a general Bell inequality for the graph state. Firstly, we show that the Bell inequality is maximally violated by graph state corresponding to some given graph. In addition, we obtain the classical bound and maximal quantum violation of Bell inequality are N + |n(i)|− 1 and \(N+(\sqrt {2}-1)(|n(i)|+1)\), respectively. Furthermore, the classical bound and maximal quantum violation of Bell inequality are dependent on the choice of the vertex for most graphs expect for complete graph.

中文翻译：

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关于图状态的贝尔不等式的注记

在本文中，我们为图状态构造了一个一般的Bell不等式。首先，我们证明了与某个给定图相对应的图状态最大程度地违反了贝尔不等式。另外，我们得到经典的界，贝尔不等式的最大量子违反为N + |。n（i）| − 1和\（N +（\ sqrt {2} -1）（| n（i）| +1）\）。此外，贝尔不等式的经典有界和最大量子违背性取决于大多数图期望完整图的顶点的选择。