The Quantum Kalman Decomposition: A Gramian Matrix Approach
Quantum Physics
2023-12-27 v1 Systems and Control
Systems and Control
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.
Cite
@article{arxiv.2312.16082,
title = {The Quantum Kalman Decomposition: A Gramian Matrix Approach},
author = {Guofeng Zhang and Jinghao Li and Zhiyuan Dong and Ian R. Petersen},
journal= {arXiv preprint arXiv:2312.16082},
year = {2023}
}
Comments
22 pages, 2 figures, submitted for publication. Comments are welcome