Linear quantum systems: poles, zeros, invertibility and sensitivity

• URL: http://arxiv.org/abs/2410.00014v1
• Date: Sat, 14 Sep 2024 14:03:48 GMT
• Title: Linear quantum systems: poles, zeros, invertibility and sensitivity
• Authors: Zhiyuan Dong, Guofeng Zhang, Heung-wing Joseph Lee, Ian R. Petersen,
• Abstract summary: The noncommutative nature of quantum mechanics imposes fundamental constraints on system dynamics. This paper investigates the zeros and poles of linear quantum systems. Two types of stable input observers are constructed for unstable linear quantum systems.
• Score: 2.7694956548319762
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The noncommutative 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. This paper aims to study this structure by investigating the zeros and poles of linear quantum systems. Firstly, it is shown 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 correspondences, we show that a linear quantum system must be Hurwitz unstable if it is strongly asymptotically left invertible. Two types of stable input observers are constructed for unstable linear quantum systems. Finally, the sensitivity of a coherent feedback network is investigated; in particular, the fundamental tradeoff between ideal input squeezing and system robustness is studied on the basis of system sensitivity analysis.

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