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

TL;DR

This paper applies quantum hypothesis testing to optimize quantum ranging, deriving fundamental limits for error probabilities and proposing measurement strategies that approach these bounds, with verification through simulations.

Contribution

It introduces a quantum hypothesis testing framework for unknown return signals in quantum ranging, identifying measurement strategies that reach or approach quantum limits.

Findings

Derived bounds for symmetric and asymmetric error probabilities in quantum ranging.

Engineered a measurement that saturates quantum bounds in some cases.

Validated theoretical predictions with numerical simulations.

Abstract

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.