Self-assisted complete analysis of three-photon hyperentangled Greenberger–Horne–Zeilinger states with nitrogen-vacancy centers in microcavities

We propose a self-assisted complete analysis scheme of three-photon hyperentangled Greenberger–Horne–Zeilinger (GHZ) states with nitrogen-vacancy (NV) centers in microcavities (NV center-cavity systems), which is used to distinguish 64 three-photon hyperentangled GHZ states entangled in polarization and spatial-mode degrees of freedom. In our scheme, only three NV center-cavity systems are required for distinguishing the 64 three-photon hyperentangled GHZ states, which is much simpler than the previous schemes. Moreover, the three-photon spatial-mode GHZ states are distinguished with the three NV center-cavity systems without affecting the hyperentangled state of three-photon system, so the three-photon polarization GHZ states can be distinguished with linear optical elements assisted by the spatial-mode entangled state of three-photon system. With our scheme, the difficulty in the experimental realization of complete analysis of hyperentangled GHZ states may be largely decreased, which could potentially improve the performance of high-capacity multi-party quantum communication.