  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.

Quantum Physics