Identification of a quantum change point

A source  assumed to prepare identical copies of a state suffers some internal alteration that makes it to start producing a different type of state.  We are interested in knowing when the change occurred assuming that it happens with equal probability at any point  of a string of N states. This an instance of multi-hypoteses discrimination for which very few results are known. I will review the optimality conditions and apply them for this task. I will compute the optimal asymptotic solution, and obtain a closed expression, which involve the use of some nice tricks. I will also compare it with (numerical) results of local protocols.