Conclusive modification of the overlap between two quantum states

The task of changing the overlap between two quantum states cannot be performed by making use of unitary evolution only. However, by means of a unitary-reduction process, it could be modified. Here we study in detail the problem of mapping two known pure states onto two other states in such a way that the overlap between the outcome states is different from the one of the initial states. We show that the modulus of the overlap can be reduced only probabilistically, whereas it can be increased deterministically. Our analysis shows that the phases of the involved overlaps play an important role in the increase of the success probability of the desired process.