  Quantum metrology studies the ultimate limit of precision in estimating a
physical quantity if quantum strategies are exploited. Here we investigate the
evolution of a two-level atom as a detector which interacts with a massless
scalar field using the master equation approach for open quantum system. We
employ local quantum estimation theory to estimate the Unruh temperature when
probed by a uniformly accelerated detector in the Minkowski vacuum. In
particular, we evaluate the Fisher information (FI) for population measurement,
maximize its value over all possible detector preparations and evolution times,
and compare its behavior with that of the quantum Fisher information (QFI). We
find that the optimal precision of estimation is achieved when the detector
evolves for a long enough time. Furthermore, we find that in this case the FI
for population measurement is independent of initial preparations of the
detector and is exactly equal to the QFI, which means that population
measurement is optimal. This result demonstrates that the achievement of the
ultimate bound of precision imposed by quantum mechanics is possible. Finally,
we note that the same configuration is also available to the maximum of the QFI
itself.
