Unitary Dilations of Discrete-Time Quantum-Dynamical Semigroups

Abstract

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.

arXiv comment32 pages, no figures

References in corpus (2)

• Dividing Quantum Channels
• Unitary Dilations of Discrete-Time Quantum-Dynamical Semigroups

Cited by in corpus (5)

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• Unitary Dilations of Discrete-Time Quantum-Dynamical Semigroups
• Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics
• Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space