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.

Automated summary

We propose a faithful and efficient hyperentanglement purification protocol for nonlocal two-photon systems in spatial-polarization-time-bin hyperentangled Bell states. The parity-check gates and swap gates in our protocol work faithfully in the spatial, polarization, and time-bin mode degrees of freedom, detecting and heralding undesirable properties caused by side leakage and finite coupling strength. The faithful parity-check gates correct qubit-flip errors efficiently in three degrees of freedom and the faithful swap gates enable the reuse of photon pairs, significantly increasing the efficiency of our hyperentanglement purification protocol. In principle, maximal hyperentanglement can be achieved by operating multiple rounds of the protocol.