Proposal for the complete high-dimensional Greenberger-Horne-Zeilinger state measurement

A theoretical proposal for the complete analysis of high-dimensional Greenberger-Horne-Zeilinger (GHZ) state is presented in this Letter. We first demonstrate the approach for the complete three-photon GHZ state measurement in three dimensions, and then generalize it to the situation of N-photon system in d dimensions. In our approach, the photonic hyperentanglement and quantum Fourier transform are both utilized. The presented proposal will be useful for the high-dimensional multi-photon quantum computation and quantum communication.