Schlichtholz, KonradKonradSchlichtholzLinowski, TomaszTomaszLinowskiWalschaers, MattiaMattiaWalschaersTreps, NicolasNicolasTrepsRudnicki, ŁukaszŁukaszRudnickiSorelli, GiacomoGiacomoSorelli2024-02-262024-02-262024https://publica.fraunhofer.de/handle/publica/46250210.1364/opticaq.502459Quantum-optimal discrimination between one and two closely separated light sources can be theoretically achieved by ideal spatial-mode demultiplexing, simply monitoring whether a photon is detected in a single antisymmetric mode. However, we show that for any imperfections of the demultiplexer, no matter how small, this simple statistical test becomes practically useless. 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.enOAjournal article