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http://hdl.handle.net/10397/14396
Title: | On realization theory of quantum linear systems | Authors: | Gough, JE Zhang, G |
Issue Date: | Sep-2015 | Source: | Automatica, Sept. 2015, v. 59, 6441, p. 139-151 | Abstract: | The purpose of this paper is to study the realization theory of quantum linear systems. It is shown that for a general quantum linear system its controllability and observability are equivalent and they can be checked by means of a simple matrix rank condition. Based on controllability and observability a specific realization is proposed for general quantum linear systems in which an uncontrollable and unobservable subspace is identified. When restricted to the passive case, it is found that a realization is minimal if and only if it is Hurwitz stable. Computational methods are proposed to find the cardinality of minimal realizations of a quantum linear passive system. It is found that the transfer function G(s) of a quantum linear passive system can be written as a fractional form in terms of a matrix function Σ(s); moreover, G(s) is lossless bounded real if and only if Σ(s) is lossless positive real. A type of realization for multi-input-multi-output quantum linear passive systems is derived, which is related to its controllability and observability decomposition. Two realizations, namely the independent-oscillator realization and the chain-mode realization, are proposed for single-input-single-output quantum linear passive systems, and it is shown that under the assumption of minimal realization, the independent-oscillator realization is unique, and these two realizations are related to the lossless positive real matrix function Σ(s). | Keywords: | Controllability Observability Quantum linear systems Realization theory |
Publisher: | Pergamon Press | Journal: | Automatica | ISSN: | 0005-1098 | DOI: | 10.1016/j.automatica.2015.06.023 | Rights: | © 2015 Elsevier Ltd. All rights reserved. © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ The following publication Gough, J. E., & Zhang, G. (2015). On realization theory of quantum linear systems. Automatica, 59, 139-151 is available at https://doi.org/10.1016/j.automatica.2015.06.023. |
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Gough_Realizatitheory_Quantum_Linear.pdf | Pre-Published version | 1.03 MB | Adobe PDF | View/Open |
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