Entangled three-state systems violate local realism more strongly than qubits: An analytical proof

In Kaszlikowski et al. [Phys. Rev. Lett. 85, 4418 (2000)], it has been shown numerically that the violation of local realism for two maximally entangled N-dimensional $(3<~N)$ quantum objects is stronger than for two maximally entangled qubits and grows with N. In this paper, we present the analytical proof of this fact for $N=3.$