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.
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