Generation of hyperentangled state encoded in three degrees of freedom

Hyperentanglement, the simultaneous entanglement in more than one degree of freedom(DOF), plays an important role in quantum communication and quantum information processing for it can effectively increase the channel capacity. Existing hyperentanglement sources mainly focus on the generation of the hyperentanglement in two DOFs. In this paper, we design the generation protocols for three kinds of hyperentanglement encoded in three DOFs with the practical coherent pulses sources, including the polarization-frequency-space hyperentanglement, the polarization-frequency-time-bin hyperentanglement, and the polarizationspace-time-bin hyperentanglement. These protocols exploit the spontaneous parametric down-conversion(SPDC) process and the Sagnac interferometer. The three protocols are all based on feasible experimental condition and may have potential applications in future hyperentanglement-based quantum communication and quantum information processing protocols.