Wireless Multihop Quantum Teleportation Utilizing a 4-Qubit Cluster State

This paper proposes a quantum routing protocol using multihop teleportation for wireless mesh backbone networks. After analyzing the quantum multihop protocol, a four-qubit cluster state is selected as the quantum channel for the protocol. The quantum channel between intermediate nodes is established through entanglement swapping, utilizing the four-qubit cluster state. Additionally, both classical and quantum routes are created in a distributed manner. We demonstrate that quantum information can be teleported hop-by-hop from the source node to the destination node. Successful quantum teleportation occurs when the sender performs Bell state measurements (BSM), while the receiver introduces auxiliary particles, applies a positive operator-valued measure (POVM), and uses a corresponding unitary transformation to recover the transmitted state. We analyze the success probability of quantum state transfer and find that the optimal success probability is achieved when $\tau_{2|1} = \frac{1}{\sqrt{2}}$. Our numerical results show the susceptibility of $P_{\text{suc}}$ to the number of hops $N$. These findings indicate that multihop teleportation using distributed wireless quantum networks with a four-qubit cluster state is feasible.