arXiv:2509.20133 · IEEE Conference on Decision and Control (CDC)

Ergodic Properties of Quantum Markov Semigroups

Nicolas Mousset, Nina H. Amini

Published Dec 9, 2025• 0 citations

Abstract

In this paper, we study the ergodic theorem for infinite-dimensional quantum Markov semigroups, originally introduced by Frigerio and Verri in 1982, and its latest version developed by Carbone and Girotti in 2021. We provide a sufficient condition that ensures exponential convergence towards the positive recurrent subspace, a well-known result for irreducible quantum Markov semigroups in finite-dimensional Hilbert spaces. Several illustrative examples are presented to demonstrate the application of the ergodic theorem. Moreover, we show that the positive recurrent subspace plays a crucial role in the study of global asymptotic stability.

DOI: 10.1109/cdc57313.2025.11312759

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