On the power of moving quantum sensors: fully flexible and noise-resilient sensing

We show that a single moving quantum sensor provides complete access to spatially correlated scalar fields. We demonstrate that with either trajectory or internal state control, one can selectively measure any linear functional, e.g. a gradient or a spatial Fourier series coefficient, while successfully eliminating {\it all} noise signals with orthogonal spatial correlation. This even exceeds the capabilities of a sensor network consisting of multiple entangled, yet spatially fixed, quantum sensors, where the number of suppressed noise signals is limited by the number of sensor positions. We show that one can achieve an improved scaling of the quantum Fisher information for moving sensors beyond the static fundamental limit of $T^2$.