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arXiv:2602.23110

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

Kaito Tojo, Takahiro Sagawa, Ken Funo

cond-mat.stat-mechquant-phSubmitted Feb 26, 2026• Announced Feb 27, 2026• 0 citations• Revised Mar 19, 2026 (v2)
v1 · Feb 26, 2026v2 · Mar 19, 2026
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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.

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9+7 pages, 3+1 figures

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Feedback can convert continuously monitored quantum jumps into a thermodynamic resource. We formulate full counting statistics for open quantum systems under unital jump feedback by incorporating the feedback maps into the tilted generator. The resulting trajectory ensemble determines both current fluctuations and the Fisher information of the measurement record. We show that feedback can enhance reservoir-parameter estimation and clock precision without necessarily changing average thermodynamic currents. This enhanced precision is not bounded by reservoir entropy production alone. By embedding the reduced dynamics in an enlarged measurement-feedback process, we derive a feedback-modified thermodynamic uncertainty relation in which the information entropy production of the feedback apparatus supplies the missing cost. A charge-monitored double quantum dot illustrates the framework: jump-conditioned feedback improves thermometry and chemical-potential sensing, and stabilizes a quantum clock defined by output-current ticks.
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