Explore the quantum fluctuation theorems under measurement and feedback in this 41-minute lecture by Takahiro Sagawa from PCS Institute for Basic Science. Delve into the generalization of fluctuation theorems in the presence of Maxwell's demon, focusing on the quantum regime and continuous quantum measurement. Discover the concept of quantum-classical-transfer (QC-transfer) entropy and its role as a quantum counterpart to classical transfer entropy. Examine the connection between quantum thermodynamics and quantum information through theoretical discussions and numerical simulations based on an experiment-numerics hybrid verification method. Cover topics such as entropy production, autonomous information processing, quantum dynamics, and stochastic QC transfer entropy. Gain insights into the fundamental link between thermodynamics and information in both classical and quantum systems.