  Quantum information theory sets the ultimate limits for any
information-processing task. In rangefinding and LIDAR, the presence or absence
of a target can be tested by detecting different states at the receiver. In
this Letter, we use quantum hypothesis testing for an unknown coherent-state
return signal in order to derive the limits of symmetric and asymmetric error
probabilities of single-shot ranging experiments. We engineer a single
measurement independent of the range, which in some cases saturates the quantum
bound and for others is presumably the best measurement to approach it. In
addition, we verify the theoretical predictions by performing numerical
simulations. This work bridges the gap between quantum information and quantum
sensing and engineering and will contribute to devising better ranging sensors,
as well as setting the path for finding practical limits for other quantum
tasks.
