Performance of coherent-state quantum target detection in the context of asymmetric hypothesis testing

Due to the difficulties of implementing joint measurements, quantum illumination schemes that are based on signal-idler entanglement are difficult to implement in practice. For this reason, one may consider quantum-inspired designs of quantum lidar/radar where the input sources are semiclassical (coherent states) while retaining the quantum aspects of the detection. The performance of these designs could be studied in the context of asymmetric hypothesis testing by resorting to the quantum Steins lemma. However, here we discuss that, for typical finite-size regimes, the second- and third-order expansions associated with this approach are not sufficient to prove quantum advantage.