Bell inequality for quNits with binary measurements

Abstract

We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are $N^2$ different binary measurements. These binary measurements are related to the intermediate states known from eavesdropping in quantum cryptography. The maximum violation by $\sqrt{N}$ is reached for the maximally entangled state. Moreover, for N=2 it coincides with the familiar CHSH-inequality.