Zhang, GuofengPetersen, IanLi, Jinghao2023-08-070018-9286http://hdl.handle.net/1885/295091The purpose of this article is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper. The spectral structure of quantum linear systems is explored, which indicates that a quantum linear system is both controllable and observable provided that it is Hurwitz stable. A new parameterization method for quantum linear systems is proposed. This parameterization is designed for the Kalman canonical form directly. Consequently, the parameters involved are in a blockwise form in correspondence with the blockwise structure of the Kalman canonical form. This parameter structure can be used to simplify various quantum control design problems. For example, necessary and sufficient conditions for the realization of quantum back-action evading (BAE) measurements are given in terms of these new parameters. Due to their blockwise nature, a small number of parameters are required for realizing quantum BAE measurements.Hong Kong Research Grant council (Grant Number: 15206915 and 15208418) 10.13039/100000181-Air Force Office of Scientific Research 10.13039/100000006-office of Naval Research (Grant Number: FA2386-16-1-4065) 10.13039/501100000923application/pdfen-AU© 2019 The authorsBack-action evading(BAE )measurementsKalman canonical formquantum linear systems202010.1109/TAC.2019.29462342022-07-24