Wireless Multihop Quantum Teleportation Utilizing a 4-Qubit Cluster State

TL;DR

The findings indicate that multihop teleportation using distributed wireless quantum networks with a four-qubit cluster state is feasible, and it is demonstrated that quantum information can be teleported hop-by-hop from the source node to the destination node.

Abstract

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 $τ_{2|1} = \frac{1}{\sqrt{2}}$. 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.

Figures (3)

• Figure 1: The quantum mesh backbone network. The dotted lines represent quantum channels while the solid lines denote classical channels. Node A is not directly entangled with the node J. However, quantum channels between them can be established via entanglement swapping.
• Figure 2: The process of establishing quantum channel. (a) Before route-finding process. (b) After route-finding process.
• Figure 3: (a) Variation of the probability of success as a function of $\tau_{1|2}$ for various $N$. The line marker "$-\cdot$", "$-$hexagram", "$-*$" and "$-\diamond$" represent $N=2$, $N=10$, $N=100$ and $N=200$ respectively. We choose $\tau_{2|1}=1/\sqrt{2}$. (b) Variation of the probability of success as a function of $\tau_{1|2}$ for various $\tau_{2|1}$. The line marker "$-\cdot$", "$-$hexagram", "$-*$" and "$-\diamond$" denote $\tau_{2|1}=1/\sqrt{2}$, $\tau_{2|1}=1/4$, $\tau_{2|1}=1/8$ and $\tau_{2|1}=1/16$ respectively. We consider $N=200$. (c) Variation of the success probability as a function of nodes number. The line marker "$-\cdot$", "$-$hexagram", "$-*$" and "$-\diamond$" denote $\tau_{1\cdot2}=1/\sqrt{2}$, $\tau_{1\cdot2}=1/4$, $\tau_{1\cdot2}=1/8$ and $\tau_{1\cdot2}=1/16$ respectively. We take $\varrho=1$ in our numerical computations.