Relevant multi-setting tight Bell inequalities for qubitsand qutrits

摘要

In the celebrated paper [D. Collins, N. Gisin, J. Phys. A Math. Gen. 37(2004) 1775], Collins and Gisin presented for the first time a three-setting Bell inequality (here we call it CG inequality for simplicity)which is relevant to the Clauser-Horne-Shimony-Holt (CHSH)inequality. Inspired by their brilliant ideas, we obtained somemulti-setting tight Bell inequalities, which are relevant to theCHSH inequality and the CG inequality. Moreover, we generalizedthe method in the paper [J.L. Chen, D.L. Deng, Phys. Rev. A 79(2009) 012115] to construct Bell inequality for qubits to higherdimensional system. Based on the generalized method, we present,for the first time, a three-setting tight Bell inequality for two qutr-its, which is maximally violated by nonmaximally entangled statesand relevant to the Collins-Gisin-Linden-Massar-Popescuinequality.