Abstract: Linear models have been used in may quantum engineering systems for example quantum opto-mechanical systems. In this talk we discuss the structure of quantum linear systems.  The Kalman canonical form for quantum linear systems is derived. A new parameterization method for quantum linear systems is proposed. This new 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 back-action evading (BAE) measurements  are given in terms of these new parameters that specify the Kalman canonical form. Due to their blockwise nature, a small number of parameters are required for realizing BAE measurements. Moreover, it is shown that a refined structure of these physical parameters reveals the noiseless subsystem and invariant subsystems of a given quantum linear system.

     Prof. Guofeng Zhang received his B.Sc. degree and M.Sc. degree from Northeastern University, Shenyang, China, in 1998 and 2000 respectively. He received a Ph.D. degree in Applied Mathematics from the University of Alberta, Edmonton, Canada, in 2005. During 2005–2006, he was a Postdoc Fellow at the University of Windsor, Windsor, Canada. He joined the School of Electronic Engineering of the University of Electronic Science and Technology of China, Chengdu, China, in 2007. From April 2010 to December 2011 he was a Research Fellow at the Australian National University. He is currently an Associate Professor in the Department of Applied Mathematics at the Hong Kong polytechnic University. His research interests include quantum information and control, sampled-data control and nonlinear dynamics.