# A Quantum Detectable Byzantine Agreement Protocol Using Only EPR Pairs
###### 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, \(|\Psi^{+}\rangle\) 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, \(|GHZ\rangle\)\(n\)-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. Byzantine Agreement; Quantum Detectable Byzantine Agreement; quantum entanglement; Bell states; quantum games +
Footnote †: journal: Accepted: 17 July 2023  
Footnote †: journal: Accepted  
uncompromised security. The unique quantum phenomena are exploited in the design of secure protocols, e.g., for key distribution, as in [7; 8; 9; 10; 11; 12; 13], for secret sharing, as in [14; 15], for cloud storage [16; 17] or blockchain [18; 19; 20]. The emerging quantum setting has inspired researchers to approach the problem of Byzantine Agreement from a quantum perspective. In an influential paper [21] in 2001, the authors introduced a variant of Byzantine Agreement, called \"Detectable Byzantine Agreement\" and gave the first quantum protocol for Detectable Byzantine Agreement. Their protocol, which tackled only the case of 3 players, used entangled qutrits in the Aharonov state. Since then, the concept of Detectable Byzantine Agreement has become widely accepted and has generated a plethora of similar works. Other early efforts include [22], where another protocol was proposed utilizing a four-qubit singlet state, and [23] that introduced a continuous variable solution to the Byzantine Agreement problem with multipartite entangled Gaussian states. More recently, notable contributions were made by [24], presenting a quantum protocol based on tripartite GHZ-like states and homodyne measurements in the continuous variable scenario, by [19], devising a protocol without entanglement, with the additional attractive feature of achieving agreement in only three rounds, and by [20], introducing a general \(n\)-party quantum protocol based on GHZ states, with possible use in a quantum blockchain network. In this work, we introduce a novel quantum protocol, named EPRQDBA, and formally prove that EPRQDBA achieves detectable Byzantine Agreement. Almost all previous analogous protocols have been cast in the form of a game, and, we, too, follow this tradition. In particular, in our protocol, the familiar protagonists [PERSON], [PERSON] and [PERSON] make one more appearance. It is instructive to mention that the pedagogical nature of games often makes expositions of difficult and technical concepts easier to understand and appreciate. Ever since their introduction in 1999 [25; 26], quantum games, have offered additional insight because quite often quantum strategies seem to achieve better results than classical ones [27; 28; 29]. The famous prisoners' dilemma game provides the most prominent example [26; 30], which also applies to other abstract quantum games [31]. The quantization of many classical systems can even apply to political structures, as was shown in [32]. **Contribution**. This paper presents a new quantum protocol for Detectable Byzantine Agreement, called EPRQDBA. Indeed there exist many sophisticated quantum protocols guaranteed to achieve Detectable Byzantine Agreement, so why a new one?