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Quantum-optimal discrimination between one and two closely separated lightsources can be achieved by ideal spatial-mode demultiplexing, simply monitoringwhether a photon is detected in a single antisymmetric mode. However, we showthat for any, no matter how small, imperfections of the demultiplexer, thissimple statistical test becomes practically useless, i.e. as good as flipping acoin. While we identify a class of separation-independent tests with vanishingerror probabilities in the limit of large numbers of detected photons, they aregenerally unreliable beyond that very limit. As a practical alternative, wepropose a simple semi-separation-independent test, which provides a method fordesigning reliable experiments, through arbitrary control over the maximalprobability of error.

Practical tests for sub-Rayleigh source discriminations with imperfect demultiplexers