Figure 3

Median of the estimated minimum-error probability \({\tilde{p}}_{err}\) as a function of the inner product s between two unknown pure states given by Eq. (11). Solid black line corresponds to the minimum-error probability \(p_{err}\) given by the Helstrom bound of Eq. (12). Solid blue dots indicate the median of \({\tilde{p}}_{err}\) calculated over 100 initial conditions for each value of s. Blue error bars indicate the interquartile range. (a) \(\eta _0=\eta _1=1/2\), (b) \(\eta _0=1/3\) and \(\eta _1=2/3\), and (c) \(\eta _0=2/5\) and \(\eta _1=3/5\). Simulations are carried out with an ensemble size \(N=50\) and total number of iterations \(k_t=50\). Asymptotic gain parameters are used.