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Information and Computation

Efficient quantum detectable weak Byzantine agreement with optimal fault-tolerant bound

Lide Xue, Wei Yang, BingRen Chen, Weilin Chen, Liusheng Huang

Published Jul 24, 2026• 0 citations
Publisher

Abstract

Quantum entanglement can be employed in some distributed communication tasks to reduce computation and communication overheads, yielding speedups over their classical counterparts. However, existing quantum Byzantine protocols often entail excessive communication and entanglement resource consumption. Conversely, classical schemes face insecurity with the impending reality of quantum computers. To address these challenges, we present a novel quantum Detectable Weak Byzantine Agreement (DWBA) protocol with high practicability, security and optimal fault-tolerance bound. For all n players, our protocol can complete the consensus of infinite classical information via fixed n + 1 -entangled qubits and a digest function, which requires infinite entanglement resources in previous schemes. Moreover, our protocol can tolerate arbitrary t ( t < n ) faulty players without necessitating any additional initial setup information (e.g., digital signature, private random coins). In terms of efficiency, our protocol only requires O (1) rounds and O ( ( n − t ) 2 ) communication complexity, constituting an order of magnitude improvement over previous protocols. In addition, the DWBA problem solved by our protocol is inherently stronger than the 3-player Detectable Byzantine Agreement (DBA) problem solved by previous protocols, and in a weaker but sufficiently practical model, our protocol can achieve Weak Byzantine Agreement (WBA).

DOI
10.1016/j.ic.2026.105497

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Quantum entanglement can be employed in some distributed communication tasks to reduce computation and communication overheads, yielding speedups over their classical counterparts. However, existing quantum Byzantine protocols often entail excessive communication and entanglement resource consumption. Conversely, classical schemes face insecurity with the impending reality of quantum computers. To address these challenges, we present a novel quantum Detectable Weak Byzantine Agreement (DWBA) protocol with high practicability, security and optimal fault-tolerance bound. For all n players, our protocol can complete the consensus of infinite classical information via fixed n + 1 -entangled qubits and a digest function, which requires infinite entanglement resources in previous schemes. Moreover, our protocol can tolerate arbitrary t ( t < n ) faulty players without necessitating any additional initial setup information (e.g., digital signature, private random coins). In terms of efficiency, our protocol only requires O (1) rounds and O ( ( n − t ) 2 ) communication complexity, constituting an order of magnitude improvement over previous protocols. In addition, the DWBA problem solved by our protocol is inherently stronger than the 3-player Detectable Byzantine Agreement (DBA) problem solved by previous protocols, and in a weaker but sufficiently practical model, our protocol can achieve Weak Byzantine Agreement (WBA).
Byzantine agreement, the underlying core of blockchain, aims to make every node in a decentralized network reach consensus. Classical Byzantine agreements unavoidably face two major problems. One is 1/3 fault-tolerance bound, which means that the system to tolerate f malicious players requires at least 3 f + 1 players. The other is the security loopholes from its classical cryptography methods. Here, we propose a Byzantine agreement framework with unconditional security to break this bound with nearly 1/2 fault tolerance due to multiparty correlation provided by quantum digital signatures. It is intriguing that quantum entanglement is not necessary to break the 1/3 fault-tolerance bound, and we show that weaker correlation, such as asymmetric relationship of quantum digital signature, can also work. Our work strictly obeys two Byzantine conditions and can be extended to any number of players without requirements for multiparticle entanglement. We experimentally demonstrate three-party and five-party consensus for a digital ledger. Our work indicates the quantum advantage in terms of consensus problems and suggests an important avenue for quantum blockchain and quantum consensus networks.
Quantum Byzantine agreement (QBA), a cornerstone of quantum blockchain, offers inherent advantages in security and fault tolerance over classical protocols, guaranteed by the laws of quantum mechanics. However, existing multiparty QBA protocols face challenges for large-scale deployment due to exponential communication complexity or reliance on complex multi-particle entanglement. To address this, we propose a multiparty circular QBA protocol that adopts a semi-decentralized architecture, leveraging circular message gathering and quantum digital signatures to achieve quadratic communication complexity and enhanced fault tolerance. Our protocol is experimentally feasible, requiring only weak coherent states, and is compatible with existing star-shaped quantum networks. Simulations conducted on a global satellite-to-ground network demonstrate that the protocol sustains high consensus rates among multiple users, even when employing different key generation protocols under realistic conditions. This work presents a scalable framework for large-scale QBA networks, establishing the foundation for a practical quantum blockchain that enables secure and fault-tolerant decentralized services.
No system entity within a contemporary distributed cyber system can be entirely trusted. Hence, the classic centralized trust management method cannot be directly applied to it. Blockchain technology is essential to achieving decentralized trust management, its consensus mechanism is useful in addressing large-scale data sharing and data consensus challenges. Herein, an n-party quantum detectable Byzantine agreement (DBA) based on the GHZ state to realize the data consensus in a quantum blockchain is proposed, considering the threat posed by the growth of quantum information technology on the traditional blockchain. Relying on the nonlocality of the GHZ state, the proposed protocol detects the honesty of nodes by allocating the entanglement resources between different nodes. The GHZ state is notably simpler to prepare than other multi-particle entangled states, thus reducing preparation consumption and increasing practicality. When the number of network nodes increases, the proposed protocol provides better scalability and stronger practicability than the current quantum DBA. In addition, the proposed protocol has the optimal fault-tolerant found and does not rely on any other presumptions. A consensus can be reached even when there are n−2 traitors. The performance analysis confirms viability and effectiveness through exemplification. The security analysis also demonstrates that the quantum DBA protocol is unconditionally secure, effectively ensuring the security of data and realizing data consistency in the quantum blockchain.
This paper presents a novel approach to distributed consensus protocols leveraging quantum entanglement and Byzantine fault tolerance. The core claim is that quantum entanglement can provide secure and efficient agreement among nodes even in the presence of malicious actors. We propose a mechanism that utilizes quantum key distribution (QKD) to establish shared entanglement between participating nodes. Subsequent quantum measurements identify faulty nodes, informing a robust consensus algorithm built upon majority voting and entanglement-based error correction. The potential advantages of this combined approach – enhanced security and efficiency compared to traditional classical methods – are explored. The research addresses the critical challenge of achieving reliable consensus in distributed systems susceptible to Byzantine attacks. This work introduces a new paradigm for consensus, potentially leading to more resilient and secure distributed applications.
To secure modern distributed digital infrastructures, quantum blockchains exploit quantum resources to achieve information-theoretic security and surpass the classical one-third fault-tolerance bound. However, existing high-fault-tolerant protocols face a fundamental scalability challenge: the blockchain trilemma imposes either exponential communication complexity or experimentally demanding multipartite entanglement. Here, we experimentally demonstrate a scalable quantum blockchain protocol based on weak coherent states that achieves an exponential reduction in quantum communication complexity. The protocol employs a circular quantum Byzantine agreement mechanism that preserves information-theoretic security while avoiding multipartite entanglement. We implement this protocol on a photonic integrated circuit platform, realizing a six-node network over commercially available telecommunication infrastructure. Compared with previous schemes, the protocol requires less than 4% of the quantum communication resources. Leveraging this advantage, we further demonstrate a quantum-secured token exchange application achieving a throughput of 805.3 transactions per second with zero failures. These results establish a practical pathway toward scalable quantum blockchain.