On the Quasi-Balanceable Class of Linear Quantum Stochastic Systems
For researchers in quantum control and model reduction, it expands the applicability of quasi-balanced truncation to active quantum systems.
The paper refines the characterization of quasi-balanceable linear quantum stochastic systems, proving that the class is strictly larger than completely passive systems and includes all systems with a pure Gaussian steady-state. A new parameterization for this class is established.
This paper concerns the recently proposed quasi-balanced truncation model reduction method for linear quantum stochastic systems. It has previously been shown that the quasi-balanceable class of systems (i.e. systems that can be truncated via the quasi-balanced method) includes the class of completely passive systems. In this work, we refine the previously established characterization of quasi-balanceable systems and show that the class of quasi-balanceable systems is strictly larger than the class of completely passive systems. In particular, we derive a novel characterization of completely passive linear quantum stochastic systems solely in terms of the controllability Gramian of such systems. Exploiting this result, we prove that all linear quantum stochastic systems with a pure Gaussian steady-state (active systems included) are all quasi-balanceable, and establish a new complete parameterization for this important class of systems. Examples are provided to illustrate our results.