  Multi-dimensional entangled states have been proven to be more powerful in
some quantum information process. In this paper, down-converted photons from
spontaneous parametric down conversion(SPDC) are used to engineer
multi-dimensional entangled states. A kind of multi-degree multi-dimensional
Greenberger-Horne-Zeilinger(GHZ) state can also be generated. The
hyper-entangled photons, which are entangled in energy-time, polarization and
orbital angular momentum (OAM), is proved to be useful to increase the
dimension of systems and investigate higher-dimensional entangled states.
