Related papers: The Quantum Kalman Decomposition: A Gramian Matrix Approach

The Quantum Kalman Decomposition: A Gramian Matrix Approach

URL: http://arxiv.org/abs/2312.16082v1
Date: Tue, 26 Dec 2023 15:10:00 GMT
Title: The Quantum Kalman Decomposition: A Gramian Matrix Approach
Authors: Guofeng Zhang and Jinghao Li and Zhiyuan Dong and Ian R. Petersen
Abstract summary: The Kalman canonical form for quantum linear systems was derived in citeZGPG18. The purpose of this paper is to present an alternative derivation by means of a Gramian matrix approach.
Score: 4.138345020595332
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The Kalman canonical form for quantum linear systems was derived in \cite{ZGPG18}. The purpose of this paper is to present an alternative derivation by means of a Gramian matrix approach. Controllability and observability Gramian matrices are defined for linear quantum systems, which are used to characterize various subspaces. Based on these characterizations, real orthogonal and block symplectic coordinate transformation matrices are constructed to transform a given quantum linear system to the Kalman canonical form. An example is used to illustrate the main results.

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