Thermodynamic uncertainty relation under continuous measurement and feedback with quantum-classical-transfer entropy

TL;DR

This paper derives a thermodynamic uncertainty relation for quantum systems under continuous measurement and feedback, revealing how information gain can improve current precision beyond traditional thermodynamic limits.

Contribution

It introduces a new TUR incorporating quantum-classical-transfer entropy, linking information gain with thermodynamic costs in quantum feedback control.

Findings

Feedback enhances current precision beyond conventional TUR bounds.

Continuous measurement with feedback suppresses entropy production.

Illustration with a driven two-level system demonstrates improved precision.

Abstract

We derive a thermodynamic uncertainty relation (TUR) under quantum continuous measurement and feedback control. By incorporating the quantum-classical-transfer entropy, which quantifies the information gained by continuous measurement, we show that the precision of currents is constrained by information-thermodynamic costs such as the entropy production and information gain. Our result shows that information gain has the potential to enhance the precision of currents beyond the bounds set by the conventional TUR. We illustrate the bound with a driven two-level system under continuous measurement and feedback, demonstrating that feedback achieves higher precision of currents while suppressing the entropy production.