  The issue of realization of the transfer functions of Linear Quantum
Stochastic Systems (LQSSs) is of fundamental importance for the practical
applications of such systems, especially as coherent controllers for other
quantum systems. So far, most works that addressed this problem have used
cascade realizations. In this work, a new method is proposed, where the
transfer function of a LQSS is realized by a series of a pre-processing linear
static network, a reduced LQSS, and a post-processing linear static network.
The introduction of the pre- and post-processing static networks leaves an
intermediate reduced LQSS with a simple input/output structure, that is
realized by a concatenation of simple cavities. A feedback connection of the
cavities through a linear static network is used to produce the correct
dynamics for the reduced system. The resulting realization provides a nice
structural picture of the system. The key mathematical tool that allows for the
construction of this realization, is an SVD-like decomposition for doubled-up
matrices in Krein spaces. Illustrative examples are provided for the theory
developed.
