  The concept of directionally unbiased optical multiports is introduced, in
which photons may reflect back out the input direction. A linear-optical
implementation is described, and the simplest three-port version studied.
Symmetry arguments demonstrate potential for unusual quantum information
processing applications. The devices impose group structures on two-photon
entangled Bell states and act as universal Bell-state processors to implement
probabilistic quantum gates acting on state symmetries. These multiports allow
optical scattering experiments to be carried out on arbitrary undirected graphs
via linear optics and raise the possibility of linear-optical information
processing using group structures formed by optical qudit states.
