Bidirectional quantum controlled teleportation in multi-hop networks: a generalized protocol for the arbitrary n-qubit state through the noisy channel

This paper introduces a bidirectional quantum controlled teleportation (BQCT) protocol within a multi-hop communication network, designed to teleport an arbitrary \(n\)-qubit state through an \(m\)-hop network framework. Utilizing the IBM Quantum (IBMQ) Experience simulation framework and the Qiskit library, we empirically substantiate the protocol's efficacy. Our findings indicate consistent teleportation across varying hop counts, though the precision of the output state diminishes with an increase in hops. This research further delves into the impact of quantum noise—namely amplitude-damping, phase-damping, bit-flip, and phase-flip—on the protocol's performance. A significant finding is that the detrimental effects of quantum noise escalate with the number of hops, with noise influence showing independence from the input state and causing an exponential decrease in output state fidelity. Thus, our analysis suggests a potential for optimizing real quantum communication systems through a balance between error reduction strategies and the maximum tolerable noise level.