  Any imaging device such as a microscope or telescope has a resolution limit,
a minimum separation it can resolve between two objects or sources; this limit
is typically defined by "Rayleigh's criterion", although in recent years there
have been a number of high-profile techniques demonstrating that Rayleigh's
limit can be surpassed under particular sets of conditions. Quantum information
and quantum metrology have given us new ways to approach measurement ; a new
proposal inspired by these ideas has now re-examined the problem of trying to
estimate the separation between two poorly resolved point sources. The "Fisher
information" provides the inverse of the Cramer-Rao bound, the lowest variance
achievable for an unbiased estimator. For a given imaging system and a fixed
number of collected photons, Tsang, Nair and Lu observed that the Fisher
information carried by the intensity of the light in the image-plane (the only
information available to traditional techniques, including previous
super-resolution approaches) falls to zero as the separation between the
sources decreases; this is known as "Rayleigh's Curse." On the other hand, when
they calculated the quantum Fisher information of the full electromagnetic
field (including amplitude and phase information), they found it remains
constant. In other words, there is infinitely more information available about
the separation of the sources in the phase of the field than in the intensity
alone. Here we implement a proof-of-principle system which makes use of the
phase information, and demonstrate a greatly improved ability to estimate the
distance between a pair of closely-separated sources, and immunity to
Rayleigh's curse.
