Network Synthesis for a Class of Mixed Quantum-Classical Linear Stochastic Systems

The purpose of this paper is to formulate and solve a synthesis problem for a class of linear quantum equations that may describe mixed quantum-classical systems. A general model and a standard model for mixed quantum-classical linear stochastic systems are proposed for our design processes and then we show how the former may be transformed into the latter, which can clearly present the internal structure of a mixed quantum-classical system. Physical realizability conditions are derived separately for the two models to ensure that they can correspond to physical systems. Furthermore, a network synthesis theory is developed for a mixed quantum-classical system of the standard form and an example is given to illustrate the theory.