Seminar: Linear quantum systems: poles, zeros, invertibility by Prof. Guofeng Zhang
The non-commutative nature of quantum mechanics imposes fundamental constraints on system dynamics, which in the linear realm, are manifested through the physical realizability conditions on system matrices. These restrictions give system matrices a unique structure. In this talk I discuss this structure by investigating the zeros and poles of linear quantum systems. Firstly, I show that -s_0 is a transmission zero if and only if s_0 is a pole of the transfer function, and -s_0 is an invariant zero if and only if s_0 is an eigenvalue of the A-matrix, of a linear quantum system. Moreover, s_0 is an output-decoupling zero if and only if -s_0 is an input-decoupling zero. Secondly, based on these zero-pole relations, we prove that a linear quantum system must be Hurwitz unstable if it is strongly asymptotically left invertible. Stable input observers are constructed for unstable linear quantum systems. Finally, the sensitivity of a coherent feedback network is investigated. We found that the well-known complementarity constraint between sensitivity and complementary sensitivity functions no longer holds in the quantum regime; instead, much richer fundamental performance limitations exist. The fundamental tradeoff between ideal input squeezing and system robustness is studied on the basis of system sensitivity analysis.
Bio:
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 in the Department of Electrical and Computer Engineering 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, Sichuan, China, in 2007. From April 2010 to December 2011, he was a Research Fellow in the School of Engineering of The Australian National University (ANU). He joined the Hong Kong Polytechnic University in December 2011 and is currently a Professor in the Department of Applied Mathematics. His research interests include quantum information, quantum control, quantum algorithms, and tensor computation.
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- Australian National University
- Canberra, Australian Capital Territory
- Australia 2601
- Building: Ian Ross Building
- Room Number: Seminar Room R214