Identifying Objects at the Quantum Limit for Super-Resolution Imaging

We consider passive imaging tasks involving discrimination between known candidate objects and investigate the best possible accuracy with which the correct object can be identified. We analytically compute quantum-limited error bounds for hypothesis tests on any database of incoherent, quasi-monochromatic objects when the imaging system is dominated by optical diffraction. We further show that object-independent linear-optical spatial processing of the collected light exactly achieves these ultimate error rates, exhibiting superior scaling than spatially-resolved direct imaging as the scene becomes more severely diffraction-limited. We apply our results to example imaging scenarios and find conditions under which super-resolution object discrimination can be physically realized.