Multipartite Continuous Variable Solution for the Byzantine Agreement Problem

We demonstrate that the Byzantine Agreement (detectable broadcast) is also solvable in the continuous-variable scenario with multipartite entangled Gaussian states and Gaussian operations (homodyne detection). Within this scheme we find that Byzantine Agreement requires a minimum amount of entanglement in the multipartite states used in order to achieve a solution. We discuss realistic implementations of the protocol, which consider the possibility of having inefficient homodyne detectors, not perfectly correlated outcomes, and noise in the preparation of the resource states. The proposed protocol is proven to be robust and efficiently applicable under such non-ideal conditions.