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arXiv · 2506.05269

State Space Decomposition of Quantum Dynamical Semigroups

Nicolas Mousset·Nina H. Amini
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Abstract

The mean evolution of an open quantum system in continuous time is described by a time continuous semigroup of quantum channels (completely positive and trace-preserving linear maps). Baumgartner and Narnhofer presented a general decomposition of the underlying Hilbert space into a sum of invariant subspaces, also called enclosures. We propose a new reading of this result, inspired by the work of Carbone and Pautrat. In addition, we apply this decomposition to a class of open quantum random walks and to quantum trajectories, where we study its uniqueness.

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Nicolas Mousset, Nina H. Amini. 2025-06-05. State Space Decomposition of Quantum Dynamical Semigroups. https://doi.org/10.1109/qccl65142.2025.11159065

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