Improvement of bidirectional controlled teleportation by using a five-qubit composite GHZ-Bell state

Abstract: Recently, Li and Nie (Int. J. Theo. Phys. 52:1630, 2013) had introduced a bidirectional controlled quantum teleportation (BCQT) protocol by using GHZ-Bell state as a quantum channel. Also, Shukla et al. (Int. J. Theo. Phys. 52:3790, 2013) had shown the Li and Nie (LN) protocol is not a BCQT scheme. In this paper, two kinds of bidirectional teleportation schemes in order to correct and improve LN protocol are presented. In the first scheme, Alice and Bob as two legitimate users can simultaneously teleport an unknown single-qubit state to each other with the help of controller Charlie. In the second scheme, Alice can transmit two-qubit entangled state to Bob and at the same time Bob can teleport single-qubit state to Alice. In both of proposed schemes the quantum channel linking users is a GHZ-Bell state.