Quantum Byzantine agreement via Hardy correlations and entanglement swapping

We present a device-independent quantum scheme for the Byzantine generals problem. The protocol is for three parties. Party $C$ is to send two identical one-bit messages to parties $A$ and $B$. The receivers $A$ and $B$ may exchange two one-bit messages informing the other party on the message received from $C$. A bit-flipping error in one of the transmissions does not allow the receiving parties to establish what was the message of $C$. Our quantum protocol is based on Hardy's argument, which uses a set of conditions impossible for classical systems, but satisfied by predictions for a unique two-qubit state. The scheme has the feature that if the messages of the Byzantine protocol are readable (that is give an unambiguous bit value for any of the receivers), then any error by $C$ (cheating by one of the commanding generals) is impossible. $A$ and $B$ do not have to exchange protocol messages to be sure of this.