Remote application of hidden operators

Alice and Bob are two distant parties. We deal with remote application on Bob's arbitrary quantum state of an operator which is immersed in a lump operator given to Alice. For such kind of task the usual method of bidirectional quantum state teleportation does not help. Shared EPR pairs with entanglement swapping do not either. We show however that the task can be performed using a GHZ state shared between Alice and Bob. We also propose a quantum scheme to control the task by a number of third parties based on sharing a multipartite GHZ state.