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Deterministic Equations for Feedback Control of Open Quantum Systems

Alberto J. B. Rosal ^1,2,*, Patrick P. Potts ³, and Gabriel T. Landi ^1,2

¹Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
²University of Rochester Center for Coherence and Quantum Science, Rochester, New York 14627, USA
³Department of Physics and Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82 CH-4056, Switzerland

^*Contact author: abezerra@ur.rochester.edu

Phys. Rev. Lett. 137, 050401 – Published 28 July, 2026

DOI: https://doi.org/10.1103/pg2p-h529

Abstract

Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of feedback. In this letter we first introduce a unifying framework, based on a single general equation, that describes all possible feedback schemes in sequentially (and continuously) measured systems, and from which all previous results follow. Next, we specialize it to the case of quantum jumps and introduce a new type of feedback based on the channel of the last detected jump, as well as the time elapsed since it occurred. Our description is experimentally grounded, and naturally allows for the introduction of realistic effects, such as time-delays in the feedback loop. We illustrate our results with two time-dependent feedback protocols conditioned on quantum-jump detections: one achieving population inversion of a two-level system against a thermal bath, and another enabling real-time reversal of quantum transitions, both admitting steady-state solutions.

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Deterministic Equations for Feedback Control of Open Quantum Systems

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