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

Abstract

The purpose of this paper is to present a network realization theory for a class of mixed quantum-classical linear stochastic systems. Two forms, the standard form and the general form, of this class of linear mixed quantum-classical systems are proposed. Necessary and sufficient conditions for their physical realizability are derived. Based on these physical realizability conditions, a network synthesis theory for this class of linear mixed quantum-classical systems is developed, which clearly exhibits the quantum component, the classical component, and their interface. An example is used to illustrate the theory presented in this paper.

Accepted version, to appear in the journal Automatica (https://www.journals.elsevier.com/automatica/), 20 pages, 5 figures. A preliminary version of the paper appeared in Proceedings of the 51st IEEE Conference on Decision and Control (CDC), pp. 1093-1098, Maui, Hawaii, USA, 2012