Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/77565
Title: The Kalman decomposition for linear quantum systems
Authors: Zhang, G 
Grivopoulos, S
Petersen, IR
Gough, JE
Keywords: Controllability
Kalman decomposition
Linear quantum systems
Observability
Issue Date: 2018
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on automatic control, 2018, v. 63, no. 2, 7942122, p. 331-346 How to cite?
Journal: IEEE transactions on automatic control 
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.
URI: http://hdl.handle.net/10397/77565
ISSN: 0018-9286
EISSN: 1558-2523
DOI: 10.1109/TAC.2017.2713343
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