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Deterministic equations for feedback control of open quantum systems. III. Full counting statistics for jump-based feedback

Alberto J. B. Rosal1,2,*, Guilherme Fiusa1,2, Patrick P. Potts3, and Gabriel T. Landi1,2

  • *Contact author: abezerra@ur.rochester.edu
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Phys. Rev. A 114, 012216 – Published 28 July, 2026

DOI: https://doi.org/10.1103/8bhb-rbjt

Abstract

In this work, we consider a general feedback protocol based on quantum-jump detections, where the last detected jump channel is stored in a memory and subsequently used to implement a feedback action, such as modifying the system Hamiltonian conditioned on the last jump. We show that the time evolution of this general protocol can be described by a Lindblad master equation defined in a hybrid classical-quantum space, where the classical part encodes the stored measurement record (memory) and the quantum part represents the monitored system. Moreover, we show that this representation can be used to fully characterize the counting statistics of a system subject to a general jump-based feedback protocol. We apply the formalism to a three-level system coupled to two thermal baths operating as a thermal machine, and we show that jump-based feedback can be used to convert the information obtained from the jump detections into work. Our framework provides analytical tools that enable the characterization of key statistical properties of any counting observable under jump-based feedback, such as the average current, noise, correlation functions, and power spectrum.

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See Also

Deterministic Equations for Feedback Control of Open Quantum Systems

Alberto J. B. Rosal, Patrick P. Potts, and Gabriel T. Landi
Phys. Rev. Lett. 137, 050401 (2026)

Deterministic equations for feedback control of open quantum systems. II. Properties of the memory function

Alberto J. B. Rosal, Patrick P. Potts, and Gabriel T. Landi
Phys. Rev. A 114, 012215 (2026)

Article Text

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Phys. Rev. A 114, 012216– Published 28 July, 2026
  • Received 14 February 2026
  • Accepted 29 June 2026
Article part of CHORUS
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