Quantum filtering and discrimination between sets of Boolean functions.

In quantum state filtering one wants to determine whether an unknown quantum state, which is chosen from a known set of states, [|psi(1)>, em leader,|psi(N)>], is either a specific state, say |psi(1)>, or one of the remaining states, [|psi(2)>, em leader,|psi(N)>]. We present the optimal solution to this problem, in terms of generalized measurements, for the case that the filtering is required to be unambiguous. As an application, we propose an efficient, probabilistic quantum algorithm for distinguishing between sets of Boolean functions, which is a generalization of the Deutsch-Jozsa algorithm.