Bidirectional Controlled Remote Implementation of an Arbitrary Single Qubit Unitary Operation with EPR and Cluster States

We present a scheme for bidirectional controlled implementation of arbitrary single qubit operations by using two EPR states and a five-qubit cluster state as the quantum channel. Alice can implement an unknown single-qubit unitary operation on the remote Bob's quantum system and at the same time, Bob can also remotely implement an arbitrary single-qubit unitary operation on Alice's quantum system if they cooperate with the controller. We also study the bidirectional controlled implementation of unitary operations belonging to the restricted sets. It is shown that receivers can prepare the target state by performing corresponding unitary operations on their entangled particles if they cooperate with the controller.