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Quantum information theory sets the ultimate limits for anyinformation-processing task. In rangefinding and LIDAR, the presence or absenceof a target can be tested by detecting different states at the receiver. Inthis Letter, we use quantum hypothesis testing for an unknown coherent-statereturn signal in order to derive the limits of symmetric and asymmetric errorprobabilities of single-shot ranging experiments. We engineer a singlemeasurement independent of the range, which in some cases saturates the quantumbound and for others is presumably the best measurement to approach it. Inaddition, we verify the theoretical predictions by performing numericalsimulations. This work bridges the gap between quantum information and quantumsensing and engineering and will contribute to devising better ranging sensors,as well as setting the path for finding practical limits for other quantumtasks.

Towards Optimal Quantum Ranging -- Hypothesis Testing for an Unknown Return Signal