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On the physical realizability of general linear quantum stochastic differential equations with complex coefficients
Published in
2009
Pages: 1422 - 1427
Abstract
This paper is concerned with the physical realizability of linear Quantum Stochastic Differential Equations (QSDEs). In a recent paper, James, Nurdin and Petersen gave necessary and sufficient conditions for the physical realizability of linear QSDEs with real coefficients. These conditions were algebraic conditions on the system state space matrices. In this paper, we first study general linear QSDEs with complex coefficients and explain how to relate them via unitary transformations to the class of linear QSDEs with real coefficients considered by James, Nurdin Petersen. We use this relation between linear QSDEs with real and complex coefficients to derive necessary and sufficient algebraic conditions for the physical realizability of the general complex linear QSDEs being considered. Then we prove the equivalence between these algebraic conditions and a condition that an associated linear system is (J, J′)-unitary. ©2009 IEEE.
About the journal
JournalProceedings of the IEEE Conference on Decision and Control
ISSN01912216
Open AccessNo
Concepts (14)
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    Algebraic conditions
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    COMPLEX COEFFICIENTS
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    PHYSICAL REALIZABILITY
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    QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS
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    REAL COEFFICIENTS
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    Sufficient conditions
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    System state
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    Unitary transformations
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    Differential equations
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    Light polarization
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    Linear systems
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    Measurement theory
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    Stochastic systems
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    Linear transformations