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

Efficient implementation of bipartite nonlocal unitary gates using prior entanglement and classical communication