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arXiv:1001.1947

Quantum Byzantine Agreement with a Single Qutrit

Mohamed Bourennane, Adán Cabello, Marek Żukowski

Published Jan 12, 2010• 6 citations
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Abstract

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.

DOI
10.48550/arxiv.1001.1947

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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.
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.
We present a solution to an old problem in distributed computing. In its simplest form, a sender has to broadcast some information to two receivers, but they have access only to pairwise communication channels. Unlike quantum key distribution, here the goal is not secrecy but agreement, and the adversary (one of the receivers or the sender himself) is not outside but inside the game. Using only classical channels this problem is provably impossible. The solution uses pairwise quantum channels and entangled qutrits.
Quantum information science breaks limitations of conventional information transfer, cryptography and computation by using quantum superpositions or entanglement as resources for information processing. Here we report on the experimental realisation of three-party quantum communication protocols using single three-level quantum system (qutrit) communication: secret-sharing, detectable Byzantine agreement and communication complexity reduction for a three-valued function. We have implemented these three schemes using the same optical fibre interferometric setup. Our realisation is easily scalable without compromising on detection efficiency or generating extremely complex many-particle entangled states. Quantum-mechanically secure communication between three different parties has been achieved by researchers in Sweden. Mohamed Bourennane and colleagues at Stockholm University achieved this by sharing a three-state quantum object across an optical fiber network. Quantum cryptography takes advantage of the unusual properties of quantum particles to achieve a degree of security beyond that possible in any classical communication system. Often this relies on linking two particles through a quantum mechanical connection known as entanglement; however, entanglement can be difficult to create. The scheme used by Bourennane's team uses just a single quantum object known as a qutrit that can exist in one of three states. The team demonstrated three different protocols known as secret sharing, detectable Byzantine agreement and communication complexity reduction. The method shows potential for scaling up to large-scale applications.
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.