  We propose a scheme for the complete differentiation of 64 three-photon
hyperentangled GHZ states in both polarization and spatial-mode degrees of
freedoms using the quantum-dot cavity system. The three-photon
hyperentangled-GHZ-state-analysis scheme can also be used to generate 3-photon
hyperentangled GHZ states. This proposed hyperentangled analysis and generation
device can serve as crucial components of the high-capacity, long-distance
quantum communication. We use quantum swapping as an example to show the
application of this device in quantum communication with polarization and
spatial-mode degrees of freedoms. Using numerical calculations, we show that
the present scheme may be feasible in strong-coupling regimes with current
technologies.
