On the Quasi-Balanceable Class of Linear Quantum Stochastic Systems

TL;DR

This paper refines the understanding of quasi-balanceable linear quantum stochastic systems, showing they include all systems with pure Gaussian steady-states, and provides new characterizations and parameterizations.

Contribution

It extends the class of quasi-balanceable systems beyond completely passive systems and offers a new characterization based on the controllability Gramian.

Findings

All systems with pure Gaussian steady-states are quasi-balanceable.

The class of quasi-balanceable systems is larger than previously known.

New parameterization for systems with pure Gaussian steady-states.

Abstract

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.