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Modern Physics Letters A

An improved quantum solution to the detectable byzantine problem

Xiaojun Wen, Yongzhi Chen, Zhi-Jia Lu, Wei Zhang, Yan-Yan Gao, Zoe L. Jiang, Junbin Fang

Published Jul 29, 2025• 0 citations
Publisher

Abstract

In distributed computing systems such as blockchain, Byzantine protocol is a practical method to solve its fault-tolerance problem. The Byzantine question has a variant called the “detectable Byzantine protocol.” This type of protocol is unsolvable in the classical field, but it can be solved using quantum physics properties in quantum systems. Based on the wonderful characteristics of quantum entanglement, a method of quantum channel detection, generation and safe distribution of digital lists is designed by using two quantum entangled states of three photons as quantum channels, so as to solve the tripartite Byzantine problem of detection more simply. Finally, the correctness and security of the scheme are analyzed.

DOI
10.1142/s0217732325500282

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In distributed computing systems such as blockchain, Byzantine protocol is a practical method to solve its fault-tolerance problem. The Byzantine question has a variant called the “detectable Byzantine protocol.” This type of protocol is unsolvable in the classical field, but it can be solved using quantum physics properties in quantum systems. Based on the wonderful characteristics of quantum entanglement, a method of quantum channel detection, generation and safe distribution of digital lists is designed by using two quantum entangled states of three photons as quantum channels, so as to solve the tripartite Byzantine problem of detection more simply. Finally, the correctness and security of the scheme are analyzed.
In distributed computing,Byzantine agreement is a practical method to solve its fault-tolerance problem.There is a variation of the Byzantine agreement which is called detectable Byzantine agreement.This kind of protocol is unsolvable by classical means,but can be solved using quantum resources——quantum entangled states.A typical quantum detectable Byzantine agreement is the GBKCW protocol.The part with the generation and distribution of the lists in the GBKCW protocol was dealed with.In order to keep the GBKCW protocol from the intercept-and-resend strategy,the property of the determination of entangled states were employed to test the sharing state between the parties.
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.
This paper proposes a novel distributed consensus algorithm utilizing quantum entanglement to achieve Byzantine fault tolerance. Traditional consensus algorithms struggle to guarantee correctness in the face of malicious actors (Byzantine faults) where nodes can arbitrarily deviate from the honest majority. This work introduces a protocol that leverages the unique properties of quantum entanglement to establish correlated states between nodes, enabling the detection and mitigation of these malicious behaviors without relying on trusted third parties or computationally intensive verification processes. The core claim is that quantum entanglement provides a provably secure and efficient mechanism for distributed consensus, offering superior resilience compared to classical approaches. The algorithm is formally described, and key mathematical components, including state transformations and probability calculations, are presented. The theoretical analysis demonstrates the algorithm's ability to converge to a correct consensus state even when a significant fraction of nodes are faulty. The use of entanglement fundamentally alters the Byzantine fault tolerance landscape, offering a pathway towards more robust and secure distributed systems.
Quantum mechanics provides several methods to generate and securely distribute private lists of numbers suitably correlated to solve the Three Byzantine Generals Problem. So far, these methods are based on three-qutrit singlet states, four-qubit entangled states, and three or two pairwise quantum key distribution channels. Here we show that the problem can be solved using a single qutrit. This scheme presents some advantages over previous schemes, and emphasizes the specific role of qutrits in basic quantum information processing.
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).
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.