State-Signal Correlations of a Continuously Monitored Superconducting Qubit

A superconducting transmon qubit undergoing driven unitary evolution is continuously monitored to observe the time evolution of its quantum state. If projective measurements are used to herald a definite initial state, the average of many measurement records displays damped Rabi oscillations. If instead the average of many measurements is conditioned on the outcome of a final post-selection measurement, the result exhibits similar damped Rabi oscillations with the exception that the damping of the signal occurs backwards in time. Such pre- and post-selections are specific examples of qubit state and signal temporal correlations and stimulate a more general discussion of the temporal correlations in stochastic quantum trajectories associated with continuous quantum measurements.