Complete hyperentangled state analysis using high-dimensional entanglement

In this paper, we present a novel method for the complete analysis of maximally hyperentangled state of photon system in two degrees of freedom (DOFs), resorting to the auxiliary high-dimensional entanglement in the third DOF. This method not only can be used for complete hyperentangled Bell state analysis of two-photon system, but also can be suitable for complete hyperentangled Greenberger-Horne-Zeilinger (GHZ) state analysis of three-photon system, and can be extended to the complete Nphoton hyperentangled GHZ state analysis. In our approach, the parity information of hyperentanglement is determined via the measurement on evolved auxiliary high-dimensional entanglement, and the relative phase information of hyperentanglement is determined via the projective measurement. Moreover, this approach can be accomplished by just using linear optics, and is significant for the investigation of photonic hyperentangled state analysis.