Cyclic Quantum Teleportation with Multi-Level of Control

We propose a cyclic quantum controlled teleportation with three controllers via a nine-qubit entangled channel state. We show that the controllers have two types of controlling levels: the same and multi-level. The former makes the controllers' combination mimic the OR or AND logic gate, i.e., each transmission in the cyclic scheme needs at least one (and does not matter which one) or all of the controllers' cooperation, respectively. While the latter makes each transmission needs a different number of controllers' cooperation combination. Furthermore, we demonstrate the protocols' channel preparation method in its application to the other controllers' combination schemes. The main advantage of the proposed protocols is that they provide a teleportation scheme with various types of controller agreement combinations that can teleport information cyclically with various levels of importance.