Further applications of the generalized phase kick-back

In our previous work, we defined a quantum algorithmic technique known as the Generalized Phase Kick-Back, or GPK, and analyzed its applications to the Deutsch–Jozsa, the Bernstein–Vazirani and the Simon p roblem. In this paper we continue analyzing the potential of this technique, defining the concept of [Formula: see text]-balanced functions and solving a new problem, which further generalizes the generalized Deutsch–Jozsa problem (the fully balanced image problem). This problem also underlines the relation between quantum computation and Boolean function theory.