Comparison of error probability bounds in quantum state discrimination

In quantum discrimination the value of the minimum error probability and the set of measurement operators which achieve this minimum are often difficult to derive. Here we compare the performance obtained by the optimal solution with the available bounds, namely the square root measurement (SRM) and the Chernoff bound, since a comparison among them has never been presented. Applied to some Gaussian states, namely to coherent states with thermal noise, it is shown that the SRM provides a much tighter bound with respect to the Chernoff bound, with a comparable numerical complexity.