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The purpose of this paper is to develop a model reduction theory for linearquantum stochastic systems that are commonly encountered in quantum optics andrelated fields, modeling devices such as optical cavities and opticalparametric amplifiers, as well as quantum networks composed of such devices.Results are derived on subsystem truncation of such systems and it is shownthat this truncation preserves the physical realizability property of linearquantum stochastic systems. It is also shown that the property of completepassivity of linear quantum stochastic systems is preserved under subsystemtruncation. A necessary and sufficient condition for the existence of abalanced realization of a linear quantum stochastic system under sympletictransformations is derived. Such a condition turns out to be very restrictiveand will not be satisfied by generic linear quantum stochastic systems, thusnecessary and sufficient conditions for relaxed notions of simultaneousdiagonalization of the controllability and observability Gramians of linearquantum stochastic systems under symplectic transformations are also obtained.The notion of a quasi-balanced realization is introduced and it is shown thatall asymptotically stable completely passive linear quantum stochastic systemshave a quasi-balanced realization. Moreover, an explicit bound for thesubsystem truncation error on a quasi-balanceable linear quantum stochasticsystem is provided. The results are applied in an example of model reduction inthe context of low-pass optical filtering of coherent light using a network ofoptical cavities.

Structures and Transformations for Model Reduction of Linear Quantum Stochastic Systems