Improvement on Quantum Bidirectional Teleportation Scheme of two ? two or two ? Three Qubit Quantum States

Recently, Ri-Gui Zhou et al. [Int. J. Theor. Phys. 59, 166-172 (2020)] proposed a scheme for bidirectional quantum teleportation of two <-> two and two <-> three qubit states by utilizing a six-qubit entangled state as a quantum channel. It is observed that the intrinsic efficiency calculated by Zhou et al. is not correct. In this improved scheme, we show that bidirectional teleportation of two <-> two and two <-> three qubit quantum states can be done by using optimized quantum resource and less consumption of classical resource. We also calculate the intrinsic efficiency of our improved scheme which is much better than the Zhou's scheme. Additionally, we also discuss about the security of the protocol.