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

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

  • Contact author: abezerra@ur.rochester.edu
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Phys. Rev. A 114, 012215 – Published 28 July, 2026

DOI: https://doi.org/10.1103/1bty-2tnq

Abstract

Feedback uses past detection outcomes to dynamically modify a quantum system and is central to quantum control. These outcomes can be stored in a memory, defined as a stochastic function of past measurements. In this work, we investigate the main properties of a general memory function subject to arbitrary feedback dynamics. We show that the memory can be treated as a classical system coupled to the monitored quantum system and that their joint evolution is described by a hybrid bipartite state. This framework allows us to introduce information-theoretic measures that quantify the correlations between the system and the memory. Furthermore, we develop a general framework to characterize the statistics of the memory, such as moments, cumulants, and correlation functions, which can be applied both to general feedback-control protocols and to monitored systems without feedback. As an application, we analyze feedback schemes based on detection events in a two-level system coupled to a thermal bath, focusing on protocols that stabilize either the excited-state population or Rabi oscillations against thermal dissipation.

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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. III. Full counting statistics for jump-based feedback

Alberto J. B. Rosal, Guilherme Fiusa, Patrick P. Potts, and Gabriel T. Landi
Phys. Rev. A 114, 012216 (2026)

Article Text

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Phys. Rev. A 114, 012215– Published 28 July, 2026
  • Received 14 February 2026
  • Accepted 29 June 2026
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