  Any bipartite nonlocal unitary operation can be carried out by teleporting a
quantum state from one party to the other, performing the unitary gate locally,
and teleporting a state back again. This paper investigates unitaries which can
be carried out using less prior entanglement and classical communication than
are needed for teleportation. Large families of such unitaries are constructed
using (projective) representations of finite groups. Among the tools employed
are: a diagrammatic approach for representing entangled states, a theorem on
the necessary absence of information at certain times and locations, and a
representation of bipartite unitaries based on a group Fourier transform.
