Quantum-optimal source discrimination with imperfect demultiplexers

Quantum-optimal discrimination between one and two closely separated light sources, relevant for, e.g., detecting spy drones and other stealth objects, can be theoretically achieved by ideal spatial demultiplexing (SPADE) of the photons emitted by the sources. However, in reality, no measurement is implemented ideally. Here, we use analytical tools to scrutinize the practical performance of SPADE for source discrimination in the presence of common experimental imperfections. First, we determine the maximum amount of noise under which SPADE remains approximately quantum-optimal. Then, we show that even when this threshold is surpassed, the efficiency of noisy SPADE still compares favorably with conventional imaging techniques. Finally, we provide explicit decision strategies for source discrimination with noisy SPADE.