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.

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The information content of a photon system can be extended by hyperentanglement, but the quality of hyperentanglement will be decreased by the complicated transmission loss and channel noise in quantum information processing. Here, an efficient measurement-based hyperentanglement distillation protocol (MB-HDP) is presented for depressing the effects of complicated transmission loss and channel noise on hyperentanglement. In the MB-HDP, the nonlocal lossy and distortion photon states are coupled to local hyperentangled Greenberger-Horne-Zeilinger (GHZ) states using parity measurement and qubit amplification device, and the decoherence caused by bit-flip (phase-flip) error, diverse transmission coefficients and transmission loss can be depressed by the successful measurement results, which can increase the quality of nonlocal hyperentangled photon state. This MB-HDP broadens the application scope of hyperentanglement distillation to nonlocal lossy and distortion photon state with a lower degree of entanglement. In addition, the MB-HDP can further improve the quality of nonlocal hyperentangled photon state by coupling multiple copies of lossy and distortion hyperentangled photon state with local hyperentangled GHZ states. This work demonstrates the ability of measurement-based method for ensuring the quality of nonlocal hyperentanglement, which can improve the integrity and capacity of long-distance quantum information processing.

Hyperentangled state analysis is an important module in high-capacity quantum communication. We present a self-assisted deterministic hyperentangled-Bell-state analysis (HBSA) scheme for photon system entangled in three degrees of freedom (DOFs), where 64 polarization-double longitudinal momentum hyperentangled Bell states are completely distinguished. In this HBSA scheme, the four first longitudinal momentum Bell states are distinguished determinately by nondestructive first longitudinal momentum Bell state analyzer, which is constructed with cross-Kerr nonlinearity medium. The 16 second longitudinal momentum-polarization hyperentangled Bell states are distinguished determinately by self-assisted second longitudinal momentum-polarization hyperentangled Bell state analyzer using linear optical elements, where the first longitudinal momentum Bell state and time-bin entangled state are used as auxiliary. Using this self-assisted method, the application of nonlinear optical resource in HBSA scheme has been largely reduced, which makes this self-assisted deterministic HBSA scheme has potential application prospects in high-capacity quantum communication.