Beating the fault-tolerance bound and security loopholes for Byzantine agreement with a quantum solution

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 $3f+1$ players. The other is the security loopholes from its classical cryptography methods. Here, we propose a strict quantum Byzantine agreement with unconditional security to break this bound with nearly $1/2$ fault tolerance due to multiparty correlation provided by quantum digital signatures. Our work strictly obeys the original Byzantine conditions and can be extended to any number of players without requirements for multiparticle entanglement. We experimentally demonstrate three-party and five-party quantum 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.