Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie-Semigroup Structures for Reachability and Control of Open Quantum
  Systems: Viewing Markovian Quantum Channels as Lie Semigroups and
  GKS-Lindblad Generators as Lie Wedge   In view of controlling finite dimensional open quantum systems, we provide a
unified Lie-semigroup framework describing the structure of completely positive
trace-preserving maps. It allows (i) to identify the Kossakowski-Lindblad
generators as the Lie wedge of a subsemigroup, (ii) to link properties of Lie
semigroups such as divisibility with Markov properties of quantum channels, and
(iii) to characterise reachable sets and controllability in open systems. We
elucidate when time-optimal controls derived for the analogous closed system
already give good fidelities in open systems and when a more detailed knowledge
of the open system (e.g., in terms of the parameters of its
Kossakowski-Lindblad master equation) is actually required for state-of-the-art
optimal-control algorithms. -- As an outlook, we sketch the structure of a new,
potentially more efficient numerical approach explicitly making use of the
corresponding Lie wedge.

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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg