Mentor initiated bi-directional asymmetric quantum teleportation protocol with hierarchical control

In this paper, we design a protocol for mutual transfer of a single-qubit state and an entangled two-qubit Bell-like state between two parties under hierarchical supervision for which there are two controllers. There is a Mentor for the protocol who is initially entangled with two separate groups of participants and by his act of measurement creates an entanglement amongst the rest of the parties for the protocol to proceed. The involvement of Mentor reduces the necessity of multipartite entanglement with a relatively large number of qubits. The generation of these two resources are described through circuit formation. The specialty of the present scheme is that it combines the role of the Mentor with those of the multiple controllers supervising at different levels into an integrated protocol. The protocol is a perfect protocol and is simulated in the Qiskit environment. Further, the efficiency of the protocol is calculated and compared with other similar ones.