  Using spontaneous parametric down conversion as a source of entangled photon
pairs, correlations are measured between the orbital angular momentum (OAM) in
a target beam (which contains an unknown object) and that in an empty reference
beam. Unlike previous studies, the effects of the object on off-diagonal
elements of the OAM correlation matrix are examined. Due to the presence of the
object, terms appear in which the signal and idler OAM do not add up to that of
the pump. Using these off-diagonal correlations, the potential for
high-efficiency object identification by means of correlated OAM states is
experimentally demonstrated for the first time. The higher-dimensional OAM
Hilbert space enhances the information capacity of this approach, while the
presence of the off-diagonal correlations allows for recognition of specific
spatial signatures present in the object. In particular, this allows the
detection of discrete rotational symmetries and the efficient evaluation of
multiple azimuthal Fourier coefficients using fewer resources than in
conventional pixel-by-pixel imaging. This represents a demonstration of sparse
sensing using OAM states, as well as being the first correlated OAM experiment
to measure properties of a real, stand-alone object, a necessary first step
toward correlated OAM-based remote sensing.
