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Two-Photon Spiral Imaging with Correlated Orbital Angular Momentum States

The concept of correlated two-photon spiral imaging is introduced. We begin by analyzing the joint orbital angular momentum (OAM) spectrum of correlated photon pairs. The mutual information carried by the photon pairs is evaluated, and it is shown that when an object is placed in one of the beam paths the value of the mutual information is strongly dependent on object shape and is closely related to the degree of rotational symmetry present. After analyzing the effect of the object on the OAM correlations, the method of correlated spiral imaging is described. We first present a version using parametric downconversion, in which entangled pairs of photons with opposite OAM values are produced, placing an object in the path of one beam. We then present a classical (correlated, but non-entangled) version. The relative problems and benefits of the classical versus entangled configurations are discussed. The prospect is raised of carrying out compressive imaging via twophoton OAM detection to reconstruct sparse objects with few measurements.