Quantum Byzantine Agreement with Tripartite Entangled States

We present a quantum protocol for resolving the detectable Byzantine agreement (BA) problem using tripartite Greenberger–Horne–Zeilinger(GHZ)-like states and homodyne measurements in the continuous variable (CV) scenario. The protocol considers the simplest (i.e., three-player) BA problem involving one broadcaster and two receivers who jointly participant in the distribution, test, and agreement phases. The GHZ-like states provide the quantum resources for implementing the primitive of BA and satisfy a priori entanglement bound. Analyses demonstrate that the proposed quantum solution adheres to the agreement, validity, and termination criteria. Conveniently, the beam splitter strategy along with photon detection offers a method for comparing quantum messages. The paper shows that a potential high-efficiency CV-based BA protocol can be achieved using standard off-the-shelf components in quantum optics, maintaining the desirable characteristics of CVs when compared with discrete-variable BA protocol.