Investigating quantum wireless multihop teleportation under decoherence

Marlon David González Ramírez, Christian Nwachioma, Adenike Grace Adepoju, Babatunde James Falaye

This research work scrutinizes quantum routing protocol with multihop teleportation for wireless mesh backbone networks, in amplitude and phase damping channels. After analyzing the quantum multihop protocol, we select a four-qubit cluster state as the quantum channel for the protocol. The quantum channel linking the intermediate nodes has been established via entanglement swapping based on four-qubit cluster state. Also, we established the classical and the quantum route in a distributed manner. We show that from the source node to the destination node, quantum information can be teleported hop-by-hop through an amplitude damping channel. We show that the quantum teleportation could be successful if the sender node performs Bell state measurements (BSM), and the receiver introduces auxiliary particles, applies positive operative value measure and then utilizes corresponding unitary transformation to recover the transmitted state. We scrutinize the success probability of transferring the quantum state through a noisy channel. We found that optimum probability would be attained if decoherence rate of amplitude damping channel ($\xi_a$) is zero or the number of hops ($N$) is above $75$. Our numerical results evince susceptibility of success probability to $\xi_a$ and $N$. It has been shown that as the decoherence increases, the fidelity exponentially decays until it vanishes. This decay is as a consequence of information loss from the system to the surrounding. However, the fidelity can be enhanced by considering fewer hops.

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