Figure 2

Relation between \(\pmb{Q_{\circlearrowleft}}\) and \(\pmb{Q_{\circlearrowright}}\) . The scatter plot was generated by computing the two Q-parameters of a set of random unitary S-matrices. The solutions at the corners \((0,0)\), \((0,3)\) and \((3,0)\) exist (for example, they are obtained respectively from \(\mathcal{I}\), \(S_{\circlearrowleft}\) and \(S_{\circlearrowright}\)); they do not appear in the plot as they are statistically not likely to occur in a set of random S matrices. In addition, the point \((2,2)\) is the well-known upper bound for reciprocal \(3\times 3\) S-matrices, see, e.g. Section 4.9 of [7].