Faithful and efficient hyperentanglement purification for spatial-polarization-time-bin photon system

We present a faithful and efficient hyperentanglement purification protocol(hyper-EPP)for nonlocal two-photon systems in spatial-polarization-time-bin hyperentangled Bell states.As the single-photon detectors can detect and herald the undesirable properties caused by side leakage and finite coupling strength,the parity-check gates and swap gates of our hyper-EPP in the spatial,polarization and time-bin mode degrees of freedom(DoFs)work faithfully.The qubit-flip errors in photon systems in three DoFs can be corrected effectively with the faithful parity-check gates and the photon pairs can be reused to distill high-fidelity ones by introducing the faithful swap gates,which greatly increases the efficiency of our hyper-EPP.Further,the maximal hyperentanglement can be obtained in principle by operating multiple rounds of the hyper-EPP.