The Kalman Decomposition for Linear Quantum Stochastic Systems

TL;DR

This paper presents a direct derivation of the Kalman decomposition for linear quantum stochastic systems using a symplectic SVD-like factorization, improving understanding of system structure in quantum control.

Contribution

It provides a direct derivation of the Kalman decomposition for linear quantum stochastic systems, utilizing a symplectic SVD-like factorization, which was previously derived indirectly.

Findings

Direct derivation of the Kalman decomposition

Utilization of symplectic SVD-like factorization

Enhanced understanding of quantum system structure

Abstract

The Kalman decomposition for Linear Quantum Stochastic Systems in the real quadrature operator representation, that was derived indirectly in [1] by the authors, is derived here directly, using the "one-sided symplectic" SVD-like factorization of [2] on the observability matrix of the system.