Complementarity and nonlocality in two-qudit systems

Complementarity and nonlocality are two characteristic traits of quantum physics that distinguish it from classical physics. In this paper, for the two-qubit case, we see that the complementarity between global and local observables in Bell's experiment sets a decisive foundation for the nonlocality of composite systems. We use the Hilbert–Schmidt norm on the commutator of two observables to quantify complementarity between them. Based on the CHSH experiment, we define a measure of complementarity Md for the two-qubit case, and extend it to two-qudit systems. Furthermore, we obtain an upper bound on Md that scales linearly in the Hilbert space dimension of the qudit.