A Quantum Measurement Engine and the Demon's Arrow of Time*

We discuss a quantum measurement engine, powered by dichotomous quantum weak measurements on a single qubit weakly coupled to a thermal reservoir, and feedback controlled by a quantum Maxwell's demon. For a demon acquiring information via quantum weak measurements, we find that the work extracted can be associated with the demon's quantum measurement arrow of time. We also discuss a realistic time-continuous operation of the engine where the measurement and feedback operations are time-continuous. In addition, we show that the engine approaches a steady state for long enough time where it operates with finite efficiency.