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In 2017, Chen et al. [Quantum Inf. Process.16 (2017) 201] proposed a scheme for cyclic quantum teleportation (CYQT) of three single-qubit information states among three participants by using six-qubit entangled state as a quantum channel. Following the work of Chen et al., we propose a new scheme for CYQT in which four participants cyclically teleport four arbitrary single-qubit information states among themselves by using two $G$-states as a quantum channel. In our scheme, reverse CYQT can also be realized throughout changing the qubit pairs to be measured by each participant. We also generalize our scheme for CYQT of $N$-qubit entangled states.

In this paper, by utilizing a nine-qubit entangled state as a quantum channel, we propose new schemes for symmetric and asymmetric cyclic controlled quantum teleportation (CYCQT). In our proposed schemes, four participants Alice, Bob, Charlie and David teleport their unknown quantum states cyclically among themselves with the help of a controller Eve. No participants can reconstruct the original states sent from the respective senders without the permission of the controller. Also, by considering same nine-qubit entangled state as a quantum channel, we propose a generalized scheme for CYCQT of multi-qubit states. In contrast to the previous CYCQT schemes involving three communicators and a controller, there are four communicators and a controller in the proposed schemes. Also, compared with previous CYCQT schemes, our proposed CYCQT schemes require less consumption of quantum resource and the intrinsic efficiency of the generalized scheme increases with the increase of number of qubits in the information states.