  Quantum-optimal discrimination between one and two closely separated light
sources can be achieved by ideal spatial-mode demultiplexing, simply monitoring
whether a photon is detected in a single antisymmetric mode. However, we show
that for any, no matter how small, imperfections of the demultiplexer, this
simple statistical test becomes practically useless, i.e. as good as flipping a
coin. While we identify a class of separation-independent tests with vanishing
error probabilities in the limit of large numbers of detected photons, they are
generally unreliable beyond that very limit. As a practical alternative, we
propose a simple semi-separation-independent test, which provides a method for
designing reliable experiments, through arbitrary control over the maximal
probability of error.
