  The detection of change points is a pivotal task in statistical analysis. In
the quantum realm, it is a new primitive where one aims at identifying the
point where a source that supposedly prepares a sequence of particles in
identical quantum states starts preparing a mutated one. We obtain the optimal
procedure to identify the change point with certainty---naturally at the price
of having a certain probability of getting an inconclusive answer. We obtain
the analytical form of the optimal probability of successful identification for
any length of the particle sequence. We show that the conditional success
probabilities of identifying each possible change point show an unexpected
oscillatory behaviour. We also discuss local (online) protocols and compare
them with the optimal procedure.
