The second law of thermodynamics under continuous quantum measurement and feedback


Toshihiro Yada, Nobuyuki Yoshioka, Takahiro Sagawa

Since the gedankenexperiment of Maxwell’s demon in 1867, the fundamental relationship between information and thermodynamics has been intensively studied mainly in classical systems, while the unified understanding involving quantum systems has not yet been established. Here, we have derived the basic principles of nonequilibrium thermodynamics in quantum systems under continuous measurement and feedback; the second law of thermodynamics and the fluctuation theorem. Our results reveal the fundamental connection between thermodynamic quantities such as heat and the newly introduced quantum-information measure called quantum-classical-transfer entropy (QC-transfer entropy). The QC-transfer entropy quantifies the flow of quantum information caused by the measurement in an operationally meaningful way, and reduces to the well-known classical transfer entropy in the classical limit. Considering the broad application of the classical transfer entropy, the QC-transfer entropy shall play a significant role in quantum information theory, e.g., in the analysis of information flow in quantum stochastic processes. Our work lays a foundation for the integrated understanding of quantum information and nonequilibrium thermodynamics, and is expected to elucidate the behavior of artificial quantum systems controlled by the cutting-edge experimental technologies.


Physical Review Letters: