Investigating nonclassicality of many qutrits by symmetric two-qubit operators

We introduce a new method of investigating qutrit nonclassicality by translating qutrit operators to symmetric two-qubit operators. We show that this procedure partially resolves the discrepancy between maximal qutrit entanglement and maximal nonclassicality of qutrit correlations. Namely we express Bell operators corresponding to qutrit Bell inequalities in terms of symmetric two-qubit operators, and analyze the maximal quantum violation of a given Bell inequality from the qubit perspective. As an example we show that the two-qutrit CGLMP(Collins-Gisin-Linden-Massar-Popescu) Bell inequality can be seen as a combination of Mermin's and CHSH (Clauser-Horne-Shimony-Holt) qubit Bell inequalities, and therefore the optimal state violating this combination differs from the one which corresponds to the maximally entangled state of two qutrits. In addition, we discuss the same problem for a three qutrit inequality. We also demonstrate that the maximal quantum violation of the CGLMP inequality follows from complementarity of correlations.