Deterministic nondestructive state analysis for polarization-spatial-time-bin hyperentanglement with cross-Kerr nonlinearity

We present a deterministic nondestructive hyperentangled Bell state analysis protocol for photons entangled in three degrees of freedom (DOFs), including polarization, spatial-mode, and time-bin DOFs. The polarization Bell state analyzer and spatial-mode Bell state analyzer are constructed by polarization parity-check quantum nondemolition detector (P-QND) and spatial-mode parity-check quantum nondemolition detector (S-QND) using cross-Kerr nonlinearity, respectively. The time-bin Bell state analyzer is constructed by the swap gate for polarization state and time-bin state of a photon (P-T swap gate) and P-QND. The Bell states analyzer for one DOF will not destruct the Bell states of other two DOFs, so the polarization-spatial-time-bin hyperentangled Bell states can be determinately distinguished without destruction. This deterministic nondestructive state analysis method has useful applications in quantum information protocols. *Project supported by the National Natural Science Foundation of China (Grant No. 11604226) and Science and Technology Program Foundation of the Beijing Municipal Commission of Education of China (Grants No. CIT&TCD201904080).