  Using no conventional measurements in position space, information extraction
rates exceeding one bit per photon are achieved by employing high-dimensional
correlated orbital angular momentum (OAM) states for object recognition. The
correlations are shown to be insensitive to axial rotation of the target
object: the information structure of an object's joint OAM coincidence spectrum
is unchanged even when the object undergoes random rotations between each
measurement. Additionally, OAM correlations alone are shown to be sufficient
for full image reconstruction of complex, off-axis objects, and novel object
symmetries are observed in the phases of OAM-object interaction transition
amplitudes. Variations in mutual information rates, due to off-axis translation
in the beam field, are studied, and it is shown that object symmetry signatures
and information rates are independent of environmental factors sufficiently far
from the beam center. The results motivate dynamic scanning applications in
contexts where symmetry and small numbers of noninvasive measurements are
desired.
