  Bell-state analysis (BSA) is essential in quantum communication, but it is
impossible to distinguish unambiguously the four Bell states in the
polarization degree of freedom (DOF) of two-photon systems with only linear
optical elements, except for the case in which the BSA is assisted with
hyperentangled states, the simultaneous entanglement in more than one DOF.
Here, we propose a scheme to distinguish completely the 16 hyperentangled Bell
states in both the polarization and the spatial-mode DOFs of two-photon
systems, by using the giant nonlinear optics in quantum dot-cavity systems.
This scheme can be applied to increase the channel capacity of long-distance
quantum communication based on hyperentanglement, such as entanglement
swapping, teleportation, and superdense coding. We use hyperentanglement
swapping as an example to show the application of this HBSA.
