Bi-directional quantum teleportation of GHZ-like states

Abstract

In this paper, we propose a method through which [Formula: see text]-qubit states can simultaneously be bi-directionally transmitted between two users. We assume that Alice and Bob, the legitimate users, each have a [Formula: see text]-qubit GHZ-like state and want to teleport it to the other party. Also, a four-qubit cluster state plays the role of the quantum channel of this bi-directional quantum teleportation. The protocol is based on the method that at first, each user, through a series of [Formula: see text] gates, converts the [Formula: see text]-qubit state into a single qubit and some [Formula: see text] qubits. Then, by means of the Bell state measurement and proper operation, the single qubit state is transferred over the channel between the two sides. By re-applying the [Formula: see text] gates on the transmitted qubits and auxiliary [Formula: see text] states, each user reconstructs the initial GHZ-like state. Finally, we investigate the effects of some kind of noises on the density matrix of the channel due to its interaction with the environment and present a method to protect the channel against the bit-flip error.