Fu Li-Bin
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009 (28), 100088 Beijing, China.
Phys Rev Lett. 2004 Apr 2;92(13):130404. doi: 10.1103/PhysRevLett.92.130404. Epub 2004 Mar 31.
We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of arbitrarily high dimensionality, which takes the same simple form as CHSH inequality for two dimensions. This inequality is optimal in the same sense as the CHSH inequality for two-dimensional systems, namely, the maximal amount by which the inequality is violated consists of the maximal resistance to noise. We also discuss the physical meaning and general definition of the correlation functions. Furthermore, by giving another specific set of the correlation functions with the same physical meaning, we realize the inequality presented by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]].
我们将克劳泽 - 霍恩 - 希莫尼 - 霍尔特（CHSH）不等式的关联函数推广到任意高维系统。基于这种推广，我们构建了任意高维二分量子系统的广义CHSH不等式，其形式与二维CHSH不等式一样简单。这个不等式在与二维系统的CHSH不等式相同的意义上是最优的，即不等式被违反的最大量由对噪声的最大抗性组成。我们还讨论了关联函数的物理意义和一般定义。此外，通过给出另一组具有相同物理意义的特定关联函数，我们实现了柯林斯等人[《物理评论快报》88, 040404 (2002)]提出的不等式。
