Logical and inequality based contextuality for qudits

Abstract: In this work we present a generalization of the recently developed Hardy-like logical proof of contextuality and of the so-called KCBS contextuality inequality for any qudit of dimension greater than three. Our approach uses compatibility graphs that can only be satisfied by qudits. We find a construction for states and measurements that satisfy these graphs and demonstrate both logical and inequality based contextuality for qudits. Interestingly, the quantum violation of the inequality is constant as dimension increases. We also discuss the issue of imprecision in experimental implementations of contextuality tests and a way of addressing this problem using the notion of ontological faithfulness.