Implementation of an ideal phase measurement with continuous, adaptive feedback*

Although the phase of an electromagnetic wave is at the heart of many algorithms in quantum metrology and communication, it is not a quantum operator in the standard sense. Nonetheless, there exists a canonical phase measurement which is conjugate to amplitude. We use a Josephson parametric amplifier and real-time adaptive measurement to perform an approximate canonical phase measurement on a superposition of zero and one photons. Measurement of single quantum trajectories allows us to independently verify the suppression of amplitude information, which guarantees that the output signal is maximally sensitive to phase. These trajectories also provide a diagnostic for optimizing the feedback system, and reconstructing the resulting measurement basis. Our experimental setup exceeds the efficiency of heterodyne detection, the most efficient technique currently used in the field.