Detecting Quantumness in the n-cycle Exclusivity Graphs

Quantum contextuality is one kind of quantumness that distinguishes quantum mechanics from classical theory. As the simplest exclusivity graph, quantum contextuality of the n-cycle graph has been reviewed, while only for odd n the quantumness can be revealed. Motivated by this, we propose the degree of non-commutativity and the degree of uncertainty to measure the quantumness in the n-cycle graphs. As desired, these two measures can detect the quantumness of any n-cycle graph when n\ge 4.