  Hyperentangled photonic states - exhibiting nonclassical correlations in
several degrees of freedom - offer improved performance of quantum optical
communication and computation schemes. Experimentally, a hyperentanglement of
transverse-wavevector and spectral modes can be obtained in a straightforward
way with multimode parametric single-photon sources. Nevertheless, experimental
characterization of such states remains challenging. Not only single-photon
detection with high spatial resolution - a single-photon camera - is required,
but also a suitable mode-converter to observe the spectral/temporal degree of
freedom. We experimentally demonstrate a measurement of a full 4-dimensional
transverse-wavevector-spectral correlations between pairs of photons produced
in the non-collinear spontaneous parametric downconversion (SPDC). Utilization
of a custom ultra-fast single-photon camera lets us characterize the two-photon
state with a high resolution and a relatively short measurement time.
