On Poles and Zeros of Linear Quantum Systems

• URL: http://arxiv.org/abs/2408.03177v1
• Date: Tue, 6 Aug 2024 13:19:18 GMT
• Title: On Poles and Zeros of Linear Quantum Systems
• Authors: Zhiyuan Dong, Guofeng Zhang, Heung-wing Joseph Lee,
• Abstract summary: Non-commutative nature of quantum mechanics imposes fundamental constraints on system dynamics. This paper investigates zeros and poses of linear quantum systems.
• Score: 2.479281189998068
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The non-commutative nature of quantum mechanics imposes fundamental constraints on system dynamics, which in the linear realm are manifested by the physical realizability conditions on system matrices. These restrictions endow system matrices with special structure. The purpose of this paper is to study such structure by investigating zeros and poses of linear quantum systems. In particular, we show that $-s_0^\ast$ is a transmission zero if and only if $s_0$ is a pole, and which is further generalized to the relationship between system eigenvalues and invariant zeros. Additionally, we study left-invertibility and fundamental tradeoff for linear quantum systems in terms of their zeros and poles.

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