  It is impossible to unambiguously distinguish the four Bell states in
polarization, resorting to linear optical elements only. Recently, the
hyperentangled Bell state, the simultaneous entanglement in more than one
degree of freedom, has been used to assist in the complete Bell-state analysis
of the four Bell states. However, if the additional degree of freedom is
qubitlike, one can only distinguish 7 from the group of 16 states. Here we
present a way to distinguish the hyperentangled Bell states completely with the
help of cross-Kerr nonlinearity. Also, we discuss its application in the
quantum teleportation of a particle in an unknown state in two different
degrees of freedom and in the entanglement swapping of hyperentangled states.
These applications will increase the channel capacity of long-distance quantum
communication.
