  We propose an experimentally feasible scheme for generating a two
$2\times4\times4$ dimensional photons hyperentangled state, entangled in
polarization, frequency and spatial mode. This scheme is mainly based on a
parametric down-conversion source and cross-Kerr nonlinearities, which avoids
the complicated uncertain post-selection. Our method can be easily expanded to
the production of hyperentangled states with more photons in multidimensions.
Hence the expectation for vast quantities of information in quantum information
processing will possibly come true. Finally, we put forward a realizable
quantum key distribution (QKD) protocol based on the high dimensional
hyperentangled state.
