Enhancing the controller's power in teleporting an arbitrary two-qubit state by using the asymmetry of the four-qubit cluster state

In this paper, we use a quantum channel that is the product of two states, the four-qubit cluster state and the three-qubit partially entangled state. This quantum channel is used as a channel in the two controlled teleportation protocols of an arbitrary two-qubit state. When the controller cooperates, both of these protocols are perfect, i.e., the total success probability and the quantum fidelity of the state received by the receiver are equal to 1. In the two controlled teleportation protocols, the number of qubits held by the controller is the same. However, depending on how the qubits in the channel are distributed to the controller, the controller's power may be entirely in or below the quantum domain. Thus, the controller's power is guaranteed when the qubits in the quantum channel are correctly distributed. On the other hand, we also show that the controller's power depends on the entanglement of the qubits that the controller holds with the rest of the qubits in the channel.