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• W2165821927 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)." @default.
• W2165821927 created "2016-06-24" @default.
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• W2165821927 date "2015-09-01" @default.
• W2165821927 modified "2023-09-27" @default.
• W2165821927 title "On realization theory of quantum linear systems" @default.
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• W2165821927 doi "https://doi.org/10.1016/j.automatica.2015.06.023" @default.
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