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
• 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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