  It is known that it is impossible to unambiguously distinguish the four Bell
states encoded in pairs of photon polarizations using only linear optics.
However, hyperentanglement, the simultaneous entanglement in more than one
degree of freedom, has been shown to assist the complete Bell analysis of the
four Bell states (given a fixed state of the other degrees of freedom). Yet
introducing other degrees of freedom also enlarges the total number of
Bell-like states. We investigate the limits for unambiguously distinguishing
these Bell-like states. In particular, when the additional degree of freedom is
qubit-like, we find that the optimal one-shot discrimination schemes are to
group the 16 states into 7 distinguishable classes, and that an unambiguous
discrimination is possible with two identical copies.
