Figure 3

The success probability of generalized sequential state discrimination when Bob, Charlie, David, and Eliot participate as receivers. Here, \(s=|\langle {\psi }_{1}|{\psi }_{2}\rangle |\) denotes the overlap between two quantum states, and we use the identical prior probability (\({q}_{1}={q}_{2}\)). The small graph shows the optimal success probability in the region of \(0 < s < 0.0035\). The solid black line shows the optimal success probability when four receivers discriminate every two pure state of Alice’s²⁷. The black dashed line as Eq. (26) shows the optimal success probability when four receivers discriminate only one of two pure states of Alice’s (Eq. (26) is a generalization of the result of Pang et al.²⁸). The red circles and the blue dots display the optimal success probability from Eq. (24). More specifically, the red circles (the blue dots) shows the optimal success probability when the constraint conditions of \({\alpha }_{1}={\alpha }_{2}\), \({\beta }_{1}={\beta }_{2}\), and \({\gamma }_{1}={\gamma }_{2}\) are (are not) added to Eq. (16). If \(s\le 0.001282\), the red circles and the blue dots coincide with the solid black line, which shows that our result agrees with that of Bergou et al.²⁷. Further, the blue dots are larger than the solid black line, but are smaller than the black dashed line. Therefore, if \(s > 0.001282\), the optimal condition of generalized sequential state discrimination does not include the constraint conditions of \({\alpha }_{1}={\alpha }_{2}\), \({\beta }_{1}={\beta }_{2}\), and \({\gamma }_{1}={\gamma }_{2}\).