Complementary Local Measurements in Nonlocality; Discriminating Genuinely High-dimensional Entanglement

Abstract

We investigate and understand nonlocality in terms of complementarity as well as entanglement. Mutual complementarity is a condition of local observables for which CHSH inequalities are maximally violated in two dimensional bipartite systems (qubits). High dimensional systems (qudits) have also been shown to violate the Bell inequalities that have recently been proposed. On the other hand, contrary to CHSH inequalities, such inequalities for qudits do not satisfy the condition of local observables being mutually unbiased when they are maximally violated. In this work, we propose an inequality satisfying the condition of mutual complementarity for local observables.