Reachable Sets from Toy Models to Controlled Markovian Quantum Systems

Gunther Dirr; Frederik vom Ende; Thomas Schulte-Herbrüggen

doi:10.1109/cdc40024.2019.9029452

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arXiv · 1905.01224

Reachable Sets from Toy Models to Controlled Markovian Quantum Systems

Gunther Dirr·Frederik vom Ende·Thomas Schulte-Herbrüggen

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Abstract

In the framework of bilinear control systems, we present reachable sets of coherently controllable open quantum systems with switchable coupling to a thermal bath of arbitrary temperature $T geq 0$. The core problem boils down to studying points in the standard simplex amenable to two types of controls that can be used interleaved: (i) permutations within the simplex, (ii) contractions by a dissipative one-parameter semigroup. Our work illustrates how the solutions of the core problem pertain to the reachable set of the original controlled Markovian quantum system. We completely characterize the case $T=0$ and present inclusions for $T>0$.

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Gunther Dirr, Frederik vom Ende, Thomas Schulte-Herbrüggen. 2019-05-03. Reachable Sets from Toy Models to Controlled Markovian Quantum Systems. https://doi.org/10.1109/cdc40024.2019.9029452

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