Thermodynamic Uncertainty Relation with Quantum Feedback

TL;DR

This paper derives a quantum thermodynamic uncertainty relation incorporating feedback control, showing how information-driven feedback can suppress fluctuations and improve precision in open quantum systems.

Contribution

It introduces a finite-time TUR for quantum systems with feedback, linking fluctuations, entropy production, and mutual information, a novel integration of information theory into quantum thermodynamics.

Findings

Feedback reduces fluctuations and enhances precision.

The TUR bounds are tightened by mutual information.

Quantum clock precision improves with feedback control.

Abstract

Fluctuations are intrinsic to microscopic systems and impose fundamental limits on nonequilibrium precision, as captured by the thermodynamic uncertainty relation (TUR), which links current fluctuations to entropy production. While feedback control is expected to further suppress fluctuations, its role within the TUR framework has remained unclear, particularly in quantum systems where control is inherently information-driven. In this Letter, we consider open quantum systems weakly coupled to a thermal environment, in which quantum jumps are continuously monitored, and Markovian feedback is applied. Using quantum mutual information to quantify the information contribution induced by feedback, we derive a finite-time TUR for arbitrary time-integrated currents in terms of entropy production and mutual information. Our results uncover how feedback control suppresses fluctuations together with thermodynamic cost and establishes a fundamental precision bound imposed by information-based control. As an application, we analyze a quantum clock model and demonstrate that the clock precision can be enhanced by feedback control in the presence of a single thermal reservoir.