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arXiv:2607.17101

GHZ-Equivalent State Distribution in Quantum Networks: Reducing Decoherence and Quantum Resource Consumption

Chun-Hsiang Wang, Chia-Wei Tsai

quant-phcs.NISubmitted Jul 19, 2026• Announced Jul 21, 2026• 0 citations
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Abstract

This study proposes a novel scheme for distributing GHZ-equivalent states across repeater-based quantum networks, with particular focus on the analysis and mitigation of decoherence effects during transmission. The proposed scheme enables remote users to share graph states, which can be leveraged to implement various quantum communication protocols, such as quantum key distribution and quantum secret sharing. Compared with existing approaches, the proposed distributed scheme requires only O(N) qubits without introducing redundant entanglement structures. Together with the linear-scaling merging procedure in both controlled gate count and qubit usage, the proposed framework supports more efficient large-scale graph state distribution. To evaluate its feasibility and correctness, this study utilizes the quantum network simulation tool, NetSquid, to implement the proposed scheme. Simulation results demonstrate that the proposed approach is both effective and practical for executing quantum communication protocols within quantum networks.

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This study proposes a novel scheme for distributing GHZ-equivalent states across repeater-based quantum networks, with particular focus on the analysis and mitigation of decoherence effects during transmission. The proposed scheme enables remote users to share graph states, which can be leveraged to implement various quantum communication protocols, such as quantum key distribution and quantum secret sharing. Compared with existing approaches, the proposed distributed scheme requires only O(N) qubits without introducing redundant entanglement structures. Together with the linear-scaling merging procedure in both controlled gate count and qubit usage, the proposed framework supports more efficient large-scale graph state distribution. To evaluate its feasibility and correctness, this study utilizes the quantum network simulation tool, NetSquid, to implement the proposed scheme. Simulation results demonstrate that the proposed approach is both effective and practical for executing quantum communication protocols within quantum networks.
Abstract Multi-particle entanglement state distribution is a crucial component for executing the quantum communication or computation protocols over quantum networks, and the graph state is an important class of multi-particle entanglement states. If the graph states can be efficiently distributed over quantum networks, the execution costs of the quantum communication or computation protocols will be greatly improved. Therefore, this study proposes an enhanced graph state transfer algorithm, which is used to distribute the graph state across a quantum network to reduce the required number of qubit measurements, quantum operation implementation, and qubit consumption without adding any additional quantum device.
Conventional Quantum Key Distribution (QKD) requires the transmission of qubits proportional to or exceeding the length of the key, as protocols such as BB84 transmit more qubits than the final key size due to basis sifting and privacy amplification. Since quantum networks are still in their infancy and have limited capacity, this overhead puts significant pressure on network resources. To address this issue, we propose a Multi-Qubit Greenberger--Horne--Zeilinger (GHZ) State-based QKD scheme that reduces the number of qubits transmitted over the quantum channel. The proposed method transmits one GHZ qubit between endpoints and reuses the resulting entanglement to convey multiple classical key bits with the help of Quantum Non-Demolition (QND) measurements. Under the stated assumptions on authenticated classical communication, local reset verification, and bounded-error QND discrimination, one can transfer LLL classical bits by generating an (L+1)-qubit GHZ state and transferring one qubit to the remote party. We verify correctness using the NetSquid quantum network simulator: the protocol achieves 100\% raw-key fidelity for keys of length up to 12 bits under both ideal conditions and depolarizing noise up to p = 0.005 per round. We further show that the proposed QKD algorithm can be extended to multi-party QKD and server-client deployment. The proposed scheme offers a transmitted-qubit-efficient, noise-tolerant alternative for bandwidth-limited quantum networks.
Many protocols of quantum information processing, like quantum key distribution or measurement-based quantum computation, 'consume' entangled quantum states during their execution. When participants are located at distant sites, these resource states need to be distributed. Due to transmission losses quantum repeater become necessary for large distances (e.g. ). Here we generalize the concept of the graph state repeater to D -dimensional graph states and to repeaters that can perform basic measurement-based quantum computations, which we call quantum routers. This processing of data at intermediate network nodes is called quantum network coding. We describe how a scheme to distribute general two-colourable graph states via quantum routers with network coding can be constructed from classical linear network codes. The robustness of the distribution of graph states against outages of network nodes is analysed by establishing a link to stabilizer error correction codes. Furthermore we show, that for any stabilizer error correction code there exists a corresponding quantum network code with similar error correcting capabilities.
Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum networks can help address this challenge by enabling the construction of large, robust, and more capable quantum computing platforms by connecting smaller quantum computers. Moreover, unlike classical systems, quantum networks can enable fully secured long-distance communication. Thus, quantum networks lie at the heart of the success of future quantum information technologies. In quantum networks, multipartite entangled states distributed over the network help implement and support many quantum network applications for communications, sensing, and computing. Our work focuses on developing optimal techniques to generate and distribute multipartite entanglement states efficiently. Prior works on generating general multipartite entanglement states have focused on the objective of minimizing the number of maximally entangled pairs while ignoring the heterogeneity of the network nodes and links as well as the stochastic nature of underlying processes. In this work, we develop a hypergraph-based linear programming framework that delivers optimal (under certain assumptions) generation schemes for general multipartite entanglement represented by graph states, under the network resources, decoherence, and fidelity constraints, while considering the stochasticity of the underlying processes. We illustrate our technique by developing generation schemes for the special cases of path and tree graph states and discuss optimized generation schemes for more general classes of graph states. Using extensive simulations over a quantum network simulator, we demonstrate the effectiveness of our developed techniques and show that they outperform prior known schemes by up to orders of magnitude.
We introduce a repeater scheme to efficiently distribute multipartite entangled states in a quantum network with optimal scaling. The scheme allows to generate graph states such as 2D and 3D cluster states of growing size or GHZ states over arbitrary distances, with a constant overhead per node/channel that is independent of the distance. The approach is genuine multipartite, and is based on the measurement-based implementation of multipartite hashing, an entanglement purification protocol that operates on a large ensemble together with local merging/connection of elementary building blocks. We analyze the performance of the scheme in a setting where local or global storage is limited, and compare it to bipartite and hybrid approaches that are based on the distribution of entangled pairs. We find that the multipartite approach offers a storage advantage, which results in higher efficiency and better performance in certain parameter regimes. We generalize our approach to arbitrary network topologies and different target graph states.
Quantum information technology has the potential to revolutionize computing, communications, and security. To fully realize its potential, quantum processors with millions of qubits are needed, which are still far from being accomplished. Thus, it is important to establish quantum networks to enable distributed quantum computing to leverage existing and near-term quantum processors into more powerful resources. This paper proposes an efficient entanglement distribution protocol for classical-quantum networks with a limited number of quantum links, enabling quantum teleportation in near-term hybrid networks. The proposed protocol uses entanglement swapping and classical network coding to distribute entanglements efficiently while overcoming bottlenecks and minimizing qubit and link usage. Experimental results show that the proposed protocol requires quantum resources that scale linearly with network size, with individual nodes only requiring a fixed number of qubits. For small network sizes of up to three transceiver pairs, the proposed protocol outperforms the benchmark by using 17% fewer qubit resources, achieving 8.8% higher accuracy, and with a 35% faster simulation time. The percentage improvement increases significantly for large network sizes. We also propose a protocol for securing entanglement distribution against malicious entanglements using quantum state encoding through rotation. Our analysis shows that this method requires no communication overhead and reduces the chance of a malicious node retrieving the teleported state to 7.2%. The achieved results point toward a protocol that enables a highly scalable, efficient, and secure near-term quantum Internet.