Routing protocol for wireless quantum multi-hop Mesh backbone network based on partially entangled GHZ state

Abstract: Quantum multi-hop teleportation is important in the field of quantum communication. In this study, we propose a quantum multi-hop communication model and a quantum routing protocol with multi-hop teleportation for wireless mesh backbone networks. Based on an analysis of quantum multi-hop protocols, a partially entangled Greenberger--Horne--Zeilinger (GHZ) state is selected as the quantum channel for the proposed protocol. Both quantum and classical wireless channels exist between two neighboring nodes along the route. With the proposed routing protocol, quantum information can be transmitted hop by hop from the source node to the destination node. Based on multi-hop teleportation based on the partially entangled GHZ state, a quantum route established with the minimum number of hops. The difference between our routing protocol and the classical one is that in the former, the processes used to find a quantum route and establish quantum channel entanglement occur simultaneously. The Bell state measurement results of each hop are piggybacked to quantum route finding information. This method reduces the total number of packets and the magnitude of air interface delay. The deduction of the establishment of a quantum channel between source and destination is also presented here. The final success probability of quantum multi-hop teleportation in wireless mesh backbone networks was simulated and analyzed. Our research shows that quantum multi-hop teleportation in wireless mesh backbone networks through a partially entangled GHZ state is feasible.

• The paper proposes a novel quantum routing protocol that uses partially entangled GHZ states for multi-hop teleportation.
• It integrates quantum and classical channels using entanglement swapping and hop-by-hop teleportation to reduce network overhead and delay.
• Analytical and simulation results demonstrate that minimizing hop count enhances the success probability of quantum information transfer.

Routing Protocol for Wireless Quantum Multi-hop Mesh Networks Using Partially Entangled GHZ States

Introduction and Motivation

Quantum communication over long distances necessitates protocols that enable reliable qubit transport across multiple hops, compensating for the decoherence and entanglement distribution limitations inherent in direct quantum links. This manuscript presents a quantum routing protocol specifically tailored for wireless mesh backbone networks, leveraging partially entangled Greenberger-Horne-Zeilinger (GHZ) states as entanglement resources for quantum teleportation. The protocol integrates quantum and classical wireless channels, implementing hop-by-hop teleportation and entanglement swapping to effect multi-hop quantum communication in mesh topologies.

Mesh Network Model and Channel Architecture

The authors extend the classical wireless mesh network (WMN) paradigm to quantum communication, introducing a backbone mesh composed of stationary route nodes and edge route nodes that interface with mobile client nodes. Each pair of neighboring nodes maintains both classical and quantum wireless channels. Entanglement resources between adjacent nodes are allocated as partially entangled GHZ states, deemed optimal due to their resource efficiency and enhanced robustness against practical non-maximal entanglement distributions.

Effective quantum communication from a source to a distant client node involves traversing a sequence of edge route and intermediate route nodes. Both classical (for measurement result dissemination) and quantum (for entanglement and state transfer) channels must be simultaneously operative for successful multi-hop teleportation.

Protocol Design: Route Establishment and Multi-hop Quantum Teleportation

The protocol consists of two principal phases: Quantum Route Request (QRR) and Quantum Route Finding (QRF). When a source node seeks to communicate with a destination to which no direct quantum route exists, it initiates a QRR to its neighboring edge route node. This request propagates through the backbone mesh, incrementing route cost metrics and updating route tables. Redundant routing loops are avoided via packet identification and source tracking.

When the edge route node adjacent to the target receives the QRR, it triggers QRF. The protocol selects the route with the minimum number of hops, exploiting the direct correlation between hop count and overall teleportation success probability for partially entangled channels. The QRF reply is unicasted in reverse along the selected route, with each node performing Bell measurements and appending results to the route reply.

Critically, the entanglement swapping (Bell measurement and associated classical information transmission) is piggybacked onto the route discovery packets, eliminating additional measurement result packets and thereby reducing the total network overhead and interface delay compared to canonical schemes. Quantum states are recovered at the destination by accumulating all measurement outcomes and applying corresponding corrective unitaries derived from the sequence of Bell outcomes.

Analytical Framework and Success Probability

The success probability analysis incorporates the degree of entanglement ($n$) for the partially entangled GHZ state and the total number of teleportation hops ($i$). The authors derive the probability of successful quantum information transfer through $i$-hop teleportations, showing a strong inverse correlation between hop count and success rate. The relevant formulas, generalized for arbitrary $n$ and $i$, are provided.

Simulation results validate that the probability of successful transmission increases with network density and transmission range, which together reduce the expected path length (i.e., the number of hops). When $n=1$ (the maximally entangled case), the protocol achieves the highest possible transmission probability, but the protocol's utility is explicitly for the regime where only partially entangled states are provisioned.

Comparative Discussion

Compared to prior schemes such as those that employ simultaneous Bell measurements at all intermediates (e.g., Wang et al.), the protocol described here introduces a sequential mechanism where entanglement swapping is synchronized with route discovery. While the sequential approach increases per-hop delay, it drastically cuts the number of packets in the network and thus reduces channel contention and routing overhead, which is paramount in bandwidth-constrained wireless quantum devices.

The explicit use of overlapping classical and quantum routing paths (rather than a strict mapping between the two) introduces additional flexibility in routing policy, permitting the balancing of physical layer constraints against logical route requirements. The protocol is compatible with arbitrary mesh topologies and does not presume regular or hierarchical structure beyond what is inherited from the underlying WMN.

Theoretical and Practical Implications

Theoretical implications include:

• Formalization of quantum routing as a joint quantum-classical pathfinding problem.
• Establishment of tight performance bounds for partially entangled GHZ-based multihop teleportation as a function of network topology and entanglement fidelity.

Practical implications include:

• Reduction in total protocol overhead and air interface delay.
• Enhanced viability of wireless quantum mesh backbones for scalable quantum networks.
• Compatibility with practical situations where entanglement generation is imperfect, negating the need for maximally entangled resources.

This framework forms the basis for future experimental realization of quantum WLAN and mesh networks, especially in mobile or ad-hoc settings, where the assumptions of fixed fiber topologies are invalid.

Future Prospects

As quantum repeater technology matures and wireless quantum transceivers become more practical, the protocol can serve as a foundational building block for adaptive and scalable quantum LAN backbones. Future research directions include:

• Integration of entanglement distillation/purification to boost $n$ dynamically.
• Adaptive routing strategies incorporating link quality estimation and traffic engineering.
• Extension to multi-party (multipartite) communication using generalized GHZ or cluster states.
• Security proofs and evaluations under adversarial and lossy conditions.

Conclusion

This work advances the state-of-the-art in quantum network protocol design by presenting a routing protocol for wireless quantum mesh networks that is specifically optimized for the realities of partial entanglement and wireless channel constraints. Simultaneous establishment of quantum links and route discovery, along with the minimization of network traffic, posit this protocol as a promising candidate for scalable, robust quantum communication in heterogeneous and dynamic environments. The analytical and simulation results underscore the necessity of route minimization for multi-hop quantum teleportation with realistic entanglement resources, providing clear guidelines for future protocol engineering.