  Entangled photons have the remarkable ability to be more sensitive to signal
and less sensitive to noise than classical light. Joint photons can sample an
object collectively, resulting in faster phase accumulation and higher spatial
resolution, while common components of noise can be subtracted. Even more, they
can accomplish this while physically separate, due to the nonlocal properties
of quantum mechanics. Indeed, nearly all quantum optics experiments rely on
this separation, using individual point detectors that are scanned to measure
coincidence counts and correlations. Scanning, however, is tedious, time
consuming, and ill-suited for imaging. Moreover, the separation of beam paths
adds complexity to the system while reducing the number of photons available
for sampling, and the multiplicity of detectors does not scale well for greater
numbers of photons and higher orders of entanglement. We bypass all of these
problems here by directly imaging collinear photon pairs with an
electron-multiplying CCD camera. We show explicitly the benefits of quantum
nonlocality by engineering the spatial entanglement of the illuminating photons
and introduce a new method of correlation measurement by converting time-domain
coincidence counting into spatial-domain detection of selected pixels. We show
that classical transport-of-intensity methods are applicable in the quantum
domain and experimentally demonstrate nearly optimal (Heisenberg-limited) phase
measurement for the given quantum illumination. The methods show the power of
direct imaging and hold much potential for more general types of quantum
information processing and control.
