Quantum Parameter Estimation for Detectors in Constantly Accelerated Motion

We analyze quantum parameter estimation by studying the dynamics of the quantum Fisher information (QFI) for two classes of parameters, acceleration and initial-state weight, in an Unruh-DeWitt detector undergoing four distinct noninertial motions: linear, cusped, catenary, and circular trajectories respectively. We assume that the detector is initialized in a pure superposition state with a weight parameter $\theta$ characterizing the probability of the detector occupying each state. Our results reveal that, over long evolution times, the QFI for the acceleration parameter converges to a nonnegative asymptotic value that depends sensitively on the trajectory, whereas the QFI for the weight parameter decays to zero as the system thermalizes. Importantly, for sufficiently large accelerations, one can attain the optimal precision in estimating the acceleration parameter within a finite interaction time, eliminating the need for infinitely long measurements. Comparing trajectories, we find that for small accelerations (relative to the detector's energy gap), linear motion yields the highest QFI for $\theta$, while for large accelerations, circular motion becomes optimal for estimating $\theta$. By contrast, circular motion offers the best precision for estimating acceleration itself in both the small- and large-acceleration regimes (the latter only at very long times). These contrasting behaviors of QFI across trajectories suggest a novel metrological protocol for inferring the underlying noninertial motion of a quantum probe.