The usefulness of the traditional apparatus of generating functions describing photon number distributions for solving current problems in quantum optics and quantum information technology is well known. At the same time, quantum mechanics implies that probabilities are underpinned by more fundamental objects—probability amplitudes. The goal of this paper is to develop an apparatus of generating functions for probability amplitudes. The proposed approach allows for the representation of all information about a quantum state in a simple, compact form. The developed method is well suited for parallel computing on supercomputers.
Bogdanov et al. (Mon,) studied this question.