Practical quantum Byzantine protocol via nearly optimal entanglement resources

Abstract

The Byzantine General Problem is a well-known problem in distributed systems, Fitzi et al. (Phys Rev Lett 87(21):217901, 2001) and Gaertner et al. (Phys Rev Lett 100(7):070504, 2008) proposed slightly weaker 3-players Byzantine protocols using quantum entanglement, respectively. However, these protocols are difficult to be applied to the n-players situation, since they require a lot of complicated entangled quantum resources, and more seriously, they all face the risk of being attacked. In this work, we present a more practical protocol than previous proposals, which can be applied to the n-players containing t traitors ($t < \frac{n}{2}$) and only requires some very simple entangled states and a few digital signatures. Our protocol matches an incentives mechanism to achieve optimal efficiency: Only one round of execution and O(mn) message complexity are required, where m is a minor parameter of the protocol. (In the worst case, the entire network requires $t+1$ rounds and $O(n^2t)$ message complexity, yet the reward mechanism will prevent this situation.)