Quantum Estimation Methods for Quantum Illumination

Quantum illumination consists in shining with quantum light on a target region immersed in a bright thermal bath with the aim of detecting the presence of a possible low-reflective object. If the signal is entangled with the receiver, then a suitable choice of the measurement offers a gain with respect to the optimal classical protocol employing coherent states. Here, we consider local strategies in which the receiver measures independently the single copies of the entangled signal. Regarding the quantum estimation of the reflectivity parameter, we show that the improvement in the signal-to-noise ratio with respect the classical case is limited to 3 dB. We relate these results to the object detection problem, showing that the gain in the error probability exponent for strategies based on the estimation of the reflectivity parameter is ruled by the quantum Fisher information. Finally, we discuss two paradigmatic examples with Gaussian and Schrodinger's cat states.