Hypercyclic systems of measurements and patterns of contextuality

Measures of contextuality in cyclic systems and the negative probabilities measure CNT 3

“…It should also be noticed that the hierarchical measure of contextuality proposed in [33] reduces to CNT 2 for cyclic systems; thus, it also satisfies the proportionality to the other measures. However, as noted in [8,13,34], the relations among these measures are not as simple in other classes of systems of random variables. In [13], one can find examples of non-cyclic systems for which CNT 1 and CNT 2 are not functions of each other, in the sense that pairs of systems can be found such that one measure obtains different values while another measure remains constant.…”

“…However, as noted in [8,13,34], the relations among these measures are not as simple in other classes of systems of random variables. In [13], one can find examples of non-cyclic systems for which CNT1 and CNT2 are not functions of each other, in the sense that pairs of systems can be found such that one measure obtains different values while another measure remains constant.…”

“…A class of examples is considered in [8,33] to show the same lack of functional relation between CNT2 and CNTF outside of cyclic systems. Lastly, in [34], some examples of hypercyclic systems of order higher than 2—cyclic systems are a special case of this class where order equals 2—show that in general there is no functional relation among any of the measures here considered.…”