  We investigate the quantum state discrimination task for sets of linear
independent pure states with an intrinsic ordering. This structured
discrimination problems allow for a novel scheme that provides a certified
level of error, that is, answers that never deviate from the true value more
than a specified distance and hence a control of the desired quality of the
results. We obtain an efficient semidefinite program and also find a general
lower bound valid for any error distance that only requires the knowledge of
optimal minimum error scheme. We apply our results to the quantum change point
and quantum state anomaly detection cases.
