Deterministic Equations for Feedback Control of Open Quantum Systems II: Properties of the memory function

• URL: http://arxiv.org/abs/2512.08085v1
• Date: Mon, 08 Dec 2025 22:30:33 GMT
• Title: Deterministic Equations for Feedback Control of Open Quantum Systems II: Properties of the memory function
• Authors: Alberto J. B. Rosal, Patrick P. Potts, Gabriel T. Landi,
• Abstract summary: We investigate the main properties of a general memory function subject to arbitrary feedback dynamics.<n>We show that the memory can be treated as a classical system coupled to a monitored quantum system.<n>We develop a general framework to characterize the statistics of the memory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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