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We use continuous weak measurements of a driven superconducting qubit toexperimentally study the information dynamics of a quantum Maxwell's demon. Weshow how information gained by a demon who can track single quantumtrajectories of the qubit can be converted into work using quantum coherentfeedback. We verify the validity of a quantum fluctuation theorem with feedbackby utilizing information obtained along single trajectories. We demonstrate, inparticular, that quantum backaction can lead to a loss of information inimperfect measurements. We furthermore probe the transition between informationgain and loss by varying the initial purity of the qubit.

Information gain and loss for a quantum Maxwell's demon