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

Improvement on Quantum bidirectional teleportation 2-2 or 2-3 qubit teleportation protocol via 6-qubit entangled state