  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.
