Cascade cavity realization for a class of complex transfer functions arising in coherent quantum feedback control

This paper presents a realization algorithm for a class of complex transfer function matrices corresponding to physically realizable linear quantum systems. The aim of the realization algorithm is to enable a coherent quantum feedback controller, which has been synthesized using methods such as quantum H^∞ control or quantum LQG control, to be constructed using optical components such as cavities and phase-shifters. The class of linear quantum systems under consideration are passive linear quantum systems which can be described purely in terms of annihilation operators. The proposed algorithm enables a complex transfer function matrix to be realized as a pure cascade connection involving only cavities and phase-shifters.