Recently, Li et al. (Int J Theor Phys: 58:1541–1545, 2019) proposed a controlled cyclic quantum teleportation method of the arbitrary two-qubit entangled states. They claimed that their method can help each of three involved participants to teleport an arbitrary two-qubit entangled state to the next participant, and at the same time, none of the involved participants can obtain the teleported state without the controller’s permission. However, this study shows that two involved participants can reconstruct the teleported states without the controller’s permission. To solve this problem, a modification is proposed here.
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