Conclusive inner product modification

The task of changing the overlap between two quantum states can not be performed by making use of a unitary evolution only. However, by means of a unitary-reduction process it can be probabilistically modified. Here we study in detail the problem of mapping two known pure states onto other two states in such a way that the final inner product between the outcome states is different from the inner product of the initial states. In this way we design an optimal non-orthogonal quantum state preparation scheme by starting from an orthonormal basis. In this scheme the absolute value of the inner product can be reduced only probabilistically whereas it can be increased deterministically. Our analysis shows that the phases of the involved inner products play an important role in the increase of the success probability of the desired process.