The Kalman Decomposition for Linear Quantum Systems
Date
2017-06-07
Authors
Zhang, Guofeng
Grivopoulos, Symeon
Petersen, Ian
Gough, J. E.
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Electrical and Electronics Engineers (IEEE Inc)
Abstract
This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws of quantum mechanics. We propose a construction method for such transformations that put the system in a Kalman canonical form. Furthermore, we uncover an interesting structure for the obtained decomposition. In the case of passive systems, it is shown that there exist only controllable/observable and uncontrollable/unobservable subsystems. In the general case, controllable/unobservable and uncontrollable/observable subsystems may also be present, but their respective system variables must be conjugate variables of each other. This decomposition naturally exposes decoherence-free modes, quantum-nondemolition modes, quantum-mechanics-free subsystems, and back-action evasion measurements in the quantum system, which are useful resources for quantum information processing, and quantum measurements. The theory developed is applied to physical examples.
Description
Keywords
Controllability, kalman decomposition, linear quantum systems, observability
Citation
Collections
Source
IEEE Transactions on Automatic Control
Type
Journal article
Book Title
Entity type
Access Statement
License Rights
Restricted until
2037-12-31
Downloads
File
Description