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Unitary dilations of discrete-time quantum-dynamical semigroups. (English) Zbl 1431.81080

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 \((T^n)_{n \in \mathbb{N}_0} \). 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.
©2019 American Institute of Physics

MSC:

81S22 Open systems, reduced dynamics, master equations, decoherence
81P47 Quantum channels, fidelity
81P40 Quantum coherence, entanglement, quantum correlations
47D07 Markov semigroups and applications to diffusion processes
47D08 Schrödinger and Feynman-Kac semigroups
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References:

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