Linear multi-particle, multi-port interferometers and their matrix representations

Abstract: Interferences in multi-path systems for single and multiple particles are theoretically analyzed. A holistic method is presented, which allows to construct the unitary transition matrix describing interferometers for any port number d and particle number n. This work has two centerpieces. First, a solution algorithm for realizing any desired unitary transformation in an interferometer for the single particle case is demonstrated. Secondly, a simple scheme for calculating the rotation matrices of beam splitters and phase shifters for multiple particles is shown. Such linear optical devices are especially important for quantum circuits and quantum information processing.