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We study the remote implementation of a unitary transformation on a qubit. Weshow the existence of non-trivial protocols (i.e., using less resources thanbidirectional state teleportation) which allow the perfect remoteimplementation of certain continuous sets of quantum operations. We prove that,up to a local change of basis, only two subsets exist that can be implementedremotely with a non-trivial protocol: Arbitrary rotations around a fixeddirection $\vec{n}$ and rotations by a fixed angle around an arbitrarydirection lying in a plane orthogonal to $\vec{n}$. The overall classicalinformation and distributed entanglement cost required for the remoteimplementation depends on whether it is a priori known to which of the twoteleportable subsets the transformation belongs to. If it is so, the optimalprotocol consumes one e-bit of entanglement and one c-bit in each direction. Ifthe subset is not known, two e-bits of entanglement need to be consumed whilethe classical channel becomes asymmetric, two c-bits are conveyed from Alice toBob but only one from Bob to Alice

Remote control of restricted sets of operations: Teleportation of angles