The Role of Complementarity in Nonlocality

Abstract

We investigate and understand in terms of complementarity as well as entanglement. Mutually complementarity is a condition of local observables for which CHSH inequalities are maximally violated in two dimensional bipartite systems. High dimensional systems (qudits) have also been shown to violate the Bell`s 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 mutually complementarity for local observables. Such an inequality consists of higher order correlations. We discuss the role of the higher order correlations in the nonlocality.