State Space Decomposition of Quantum Dynamical Semigroups

• URL: http://arxiv.org/abs/2506.05269v1
• Date: Thu, 05 Jun 2025 17:28:22 GMT
• Title: State Space Decomposition of Quantum Dynamical Semigroups
• Authors: Nicolas Mousset, Nina H. Amini,
• Abstract summary: Mean evolution of an open quantum system in continuous time is described by a time continuous semigroup of quantum channels.<n>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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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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