  We propose a practical quantum cryptographic scheme which combines high
information capacity, such as provided by high-dimensional quantum
entanglement, with the simplicity of a two-dimensional
Clauser-Horne-Shimony-Holt (CHSH) Bell test for security verification. By
applying a state combining entanglement in a two-dimensional degree of freedom,
such as photon polarization, with high-dimensional correlations in another
degree of freedom, such as photon orbital angular momentum (OAM) or path, the
scheme provides a considerably simplified route towards security verification
in quantum key distribution (QKD) aimed at exploiting high-dimensional quantum
systems for increased secure key rates. It also benefits from security against
collective attacks and is feasible using currently available technologies.
