Synthesis and structure of mixed quantum-classical linear 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. We propose a standard model for mixed quantum-classical linear stochastic systems for the design process, which can present the internal structure of a mixed quantum-classical system. Physical realizability conditions are derived for the standard model to ensure that it can correspond to a physical system. Furthermore, a network synthesis theory for a mixed quantum-classical system of the standard form has been developed. An example is given to illustrate the results.