Controller-Independent Bidirectional Direct Communication with Four-Qubit Cluster States

We propose a feasible scheme for implementing bidirectional quantum direct communication protocol using four-qubit cluster states. In this scheme, the quantum channel between the sender Alice and the receiver Bob consists of an ordered sequence of cluster states which are prepared by Alice. After ensuring the security of quantum channel, according to the secret messages, the sender will perform the unitary operation and the receiver can obtain different secret messages in a deterministic way.