Sub-wavelength quantum imaging

The resolution limit of standard imaging techniques is expressed by the Rayleigh criterion, which states that two point-like sources are difficult to resolve if their transverse separation is smaller that the Rayleigh length. While the criterion is useful in the case of direct detection imaging, other measurement techniques may not be subject to this limitation. Here we consider the use of imaging to estimate the distance between two incoherent point sources. In this framework, the Rayleigh criterion manifests itself through the so-called Rayleigh curse. The latter expresses the fact that the statistical error in the estimation increases for sub-wavelength separation. Here we show that, in the regime of weak signals, a structured measurement obtained by concatenating a linear interferometer with on-off photo-detection is immune to the Rayleigh curse. In this way we clarify the relation between imaging and interferometry, and establish the optimality of linear interferometry for an arbitrary number of incoherent sources.