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Hyperentanglement, the entanglement in several degrees of freedom (DOFs) of aquantum system, has attracted much attention as it can be used to increase boththe channel capacity of quantum communication and its security largely. Here,we present the first scheme to completely distinguish the hyperentangled Bellstates of two-photon systems in three DOFs with the help of cross-Kerrnonlinearity without destruction, including two longitudinal momentum DOFs andthe polarization DOF. We use cross-Kerr nonlinearity to construct quantumnondemolition detectors which can be used to make a parity-check measurementand analyze Bell states of two-photon systems in different DOFs. Our completescheme for two-photon six-qubit hyperentangled Bell-state analysis may beuseful for the practical applications in quantum information, especially inlong-distance high-capacity quantum communication.

Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity