Nonlocality of partially entangled two qutrits by genuinely high-dimensional inequalities

Abstract

We consider genuinely high-dimensional Bell inequalities such as CGLMP and SLK and numerically investigate the relations among complementarity, entanglement and nonlocality of the CGLMP and SLK inequalities for two qutrits. CGLMP inequality gives maximal violation for partially entangled states while the SLK inequality gives maximal violation for a maximally entangled state. The degree of complementarity of local observables when obtaining the maximal violation of these inequalities are less than 1, implying that local observables are not mutually unbiased measurements for these high-dimensional nonlocality tests.