  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.
