Optical quantum super-resolution imaging and hypothesis testing

Estimating the angular separation between two incoherent sources below the diffraction limit is challenging. Hypothesis testing and quantum state discrimination techniques are used to super-resolve sources of different brightness with a simple optical interferometer.Estimating the angular separation between two incoherent thermal sources is a challenging task for direct imaging, especially at lengths within the diffraction limit. Moreover, detecting the presence of multiple sources of different brightness is an even more severe challenge. We experimentally demonstrate two tasks for super-resolution imaging based on hypothesis testing and quantum metrology techniques. We can significantly reduce the error probability for detecting a weak secondary source, even for small separations. We reduce the experimental complexity to a simple interferometer: we show (1) our set-up is optimal for the state discrimination task, and (2) if the two sources are equally bright, then this measurement can super-resolve their angular separation. Using a collection baseline of 5.3 mm, we resolve the angular separation of two sources placed 15 mu m apart at a distance of 1.0 m with a 1.7% accuracy - an almost 3-orders-of-magnitude improvement over shot-noise limited direct imaging.