Quantum Fluctuation Theorem under Continuous Measurement and Feedback*

The fluctuation theorem has been thoroughly generalized under various feedback setups in classical systems, revealing the relationship between classical information and nonequilibrium thermodynamics. In this work, we derive the quantum fluctuation theorem in an intriguing and unexplored situation, namely under continuous measurement and feedback. In order to quantify the quantum information obtained by continuous measurement, we newly introduce the operationally meaningful information measure, which we name quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy is the quantum counterpart of the transfer entropy, which is commonly used in classical time series analysis. We also show a numerical demonstration, and propose an experiment-numerics hybrid verification method of our theoretical results. Our work indicates the general relationship between quantum information flow and quantum dissipation, which can be tested experimentally with the state-of-the-art quantum technologies.