Unitary dilations of discrete-time quantum-dynamical semigroups

We show that the discrete-time evolution of an open quantum system generated by a single quantum channel T can be embedded in the discrete-time evolution of an enlarged closed quantum system, i.e., we construct a unitary dilation of the discrete-time quantum-dynamical semigroup (Tn)n∈N0. In the case...

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Bibliographic Details
Published in:Journal of mathematical physics 2019-12, Vol.60 (12)
Main Authors: vom Ende, Frederik, Dirr, Gunther
Format: Article
Language:English
Subjects:
Commuting
Control systems
Dilation
Discrete time systems
Embedded systems
Evolution
Physics
Quantum theory
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Summary:We show that the discrete-time evolution of an open quantum system generated by a single quantum channel T can be embedded in the discrete-time evolution of an enlarged closed quantum system, i.e., we construct a unitary dilation of the discrete-time quantum-dynamical semigroup (Tn)n∈N0. In the case of a cyclic channel T, the auxiliary space may be chosen (partially) finite-dimensional. We further investigate discrete-time quantum control systems generated by finitely many commuting quantum channels and prove a similar unitary dilation result as in the case of a single channel.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5095868