Mentor initiated Bi-directional Hybrid quantum Communication Protocol

In this paper, we present a hybrid bidirectional controlled quantum communication protocol between two parties, initiated by a Mentor. Initially, the two main parties and the controller do not share a common quantum entanglement; instead, each party shares entanglement separately with the Mentor. The Mentor's actions create entanglement among the two parties and the controller. The protocol operates deterministically in the absence of environmental noise. Furthermore, we analyze the effects of various types of noises on the protocol, calculate the fidelity, and study how fidelity varies with different parameters. We also provide a theoretical description of the generation of the initial entangled channel used in the protocol. The quantum circuits for entanglement generation and also of the entire protocol are presented. To verify the protocol, these quantum circuits are executed on a real IBM quantum computer.