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.
@article{arxiv.quant-ph/0502003,
title = {Engineering of multi-dimensional entangled states of photon pairs using hyper-entanglement},
author = {Xi-Feng Ren and Guo-Ping Guo and Jian Li and Chuan-Feng Li and Guang-Can Guo},
journal= {arXiv preprint arXiv:quant-ph/0502003},
year = {2015}
}