Realization Theory for Linear Dynamical Quantum Systems

Abstract

This chapter presents a realization/network synthesis theory for linear quantum systems. This theory addresses the question of how one can go from an abstract description of a linear quantum system to a concrete realization of the system using quantum optical devices. Two distinct types of realization problems are introduced and treated: the strict (or hard) realization problem and the transfer function (or soft) realization problem. The system to be realized is decomposed into simpler subsystems, and how these subsystems can be realized, at least approximately, in the quantum optical setting is developed. In particular, it is shown that simpler realizations can be obtained for completely passive linear quantum systems.