Full-field quantum correlations of spatially entangled photons

Spatially entangled twin photons allow the study of high-dimensional entanglement, and the Laguerre-Gauss modes are the most commonly used basis to discretize the single-photon mode spaces. In this basis, to date only the azimuthal degree of freedom has been investigated experimentally due to its fundamental and experimental simplicity. We show that the full spatial entanglement is indeed accessible experimentally; i.e., we have found practicable radial detection modes with negligible cross correlations. This allows us to demonstrate hybrid azimuthal-radial quantum correlations in a Hilbert space with more than 100 dimensions per photon.