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arXiv:2306.10825 · Applied Sciences

A Quantum Detectable Byzantine Agreement Protocol Using Only EPR Pairs

Theodore Andronikos, Alla Sirokofskich

Published Jul 20, 2023• 10 citations
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Abstract

In this paper, we introduce a new quantum protocol for Detectable Byzantine Agreement. What distinguishes the proposed protocol among similar quantum protocols, is the fact that it uses only EPR pairs, and, in particular, |Ψ+⟩ pairs. There are many sophisticated quantum protocols that guarantee Detectable Byzantine Agreement, but they do not easily lend themselves to practical implementations, due to present-day technological limitations. For a large number n of players, |GHZ⟩n-tuples, or other more exotic entangled states, are not easy to produce, a fact which might complicate the scalability of such protocols. In contrast, Bell states are, undoubtedly, the easiest to generate among maximally entangled states. This will, hopefully, facilitate the scalability of the proposed protocol, as only EPR pairs are required, irrespective of the number n of players. Finally, we mention that, even for arbitrary many players n, our protocol always completes in a constant number of rounds, namely 4.

DOI
10.3390/app13148405

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In this paper, we introduce a new quantum protocol for Detectable Byzantine Agreement. What distinguishes the proposed protocol among similar quantum protocols, is the fact that it uses only EPR pairs, and, in particular, |Ψ+⟩ pairs. There are many sophisticated quantum protocols that guarantee Detectable Byzantine Agreement, but they do not easily lend themselves to practical implementations, due to present-day technological limitations. For a large number n of players, |GHZ⟩n-tuples, or other more exotic entangled states, are not easy to produce, a fact which might complicate the scalability of such protocols. In contrast, Bell states are, undoubtedly, the easiest to generate among maximally entangled states. This will, hopefully, facilitate the scalability of the proposed protocol, as only EPR pairs are required, irrespective of the number n of players. Finally, we mention that, even for arbitrary many players n, our protocol always completes in a constant number of rounds, namely 4.
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).
In this paper, we propose a protocol of quantum communication to achieve Byzantine agreement among multiple parties. Our protocol's striking feature compared to the existing protocols is that we do not use entanglement to achieve the agreement. The role played by entangled states in other protocols is replaced in our protocol by a group of semi-honest list distributors. Such a replacement makes the implementation of our protocol more feasible. Moreover, our protocol is efficient in the sense that it achieves agreement in only three rounds which is a significant improvement with respect to the alternative agreement protocol not using entanglement. In the first round, a list of numbers that satisfies some special properties is distributed to every participant by list distributors via quantum secure communication. Then, in the second and third rounds, those participants exchange some information to reach an agreement.
Quantum communication resources offer significant advantages for fault-tolerant distributed protocols, particularly in Byzantine Agreement (BA), where reliability against adversarial interference is essential. Quantum Detectable Byzantine Agreement (QDBA) enables consensus protocols that surpass classical limitations by leveraging entangled quantum states. In this work, we focus on the practical realization of QDBA using Einstein-Podolsky-Rosen (EPR) pairs, the simplest maximally entangled quantum resources, making the protocol experimentally accessible across current quantum hardware platforms. We present a comprehensive computational study of the EPRQDBA protocol under realistic quantum network conditions, utilizing the Aliro Quantum Network Simulator to evaluate the performance and robustness of the protocol. Our simulations systematically explore the protocol's parameter space --including variations in network size, traitorous node count, the amount of entanglement consumed in the protocol, and physically motivated noise models tailored specifically for superconducting and photonic qubit technologies. Through extensive numerical experiments, we provide insights into how these physically realistic parameters impact protocol performance, establishing critical thresholds and optimal operational regimes for experimental implementations. This work bridges theoretical advances in quantum consensus protocols with practical network implementations, offering a concrete reference for experimentalists. Our findings serve as a guideline for evaluating and optimizing QDBA implementations in realistic, noisy environments.
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.