A network synthesis theorem for linear dynamical quantum stochastic systems

In this paper we introduce a network synthesis theorem for linear dynamical quantum stochastic systems that are encountered in linear quantum optics and in phenomenological models of quantum linear circuits. In particular, such a theorem will be important in the physical realization of coherent/fully quantum linear stochastic controllers for quantum control. We show how general linear dynamical quantum stochastic systems can be systematically constructed by assembling an appropriate interconnection of one degree of freedom open quantum harmonic oscillators and, in the quantum optics setting, provide an explicit illustrative example of the systematic synthesis of a two degrees of freedom open quantum harmonic oscillator.