Measurement-Based Feedback of Open Quantum Systems: A Control-Theoretic Review and Tutorial

• URL: http://arxiv.org/abs/2609.06111v1
• Date: Sat, 05 Sep 2026 14:18:59 GMT
• Title: Measurement-Based Feedback of Open Quantum Systems: A Control-Theoretic Review and Tutorial
• Abstract summary: This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems.<n>Main analysis is focused on finite-dimensional systems governed by diffusive master equations.<n>We discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics.
• Score: 13.83570320951482
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems, with the main analysis focused on finite-dimensional systems governed by diffusive stochastic master equations. We introduce the relevant state-space, invariant-subspace, and quantum non-demolition structures, interpret quantum filtering as nonlinear observer dynamics, and review open-loop asymptotics, filter stability, state-feedback stabilization, robustness, and reduced-order observer-based control. Particular emphasis is placed on a recurrence--contraction framework, in which Hamiltonian feedback removes non-target invariant obstructions while measurement-induced dynamics provide local exponential contraction. Although the detailed analysis is developed for finite-dimensional diffusive models, the underlying measurement--estimation--feedback architecture is relevant across a broad range of quantum platforms. We further discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics, practical stability, optimal control, and learning-based design. By organizing these developments around invariance, estimation, recurrence, and contraction, the review provides a tutorial bridge between measurement-based quantum feedback and nonlinear stochastic control.

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