Experimental Demonstration of a Quantum Protocol for Byzantine Agreement and Liar Detection

We introduce a new quantum protocol for solving detectable Byzantine agreement (also called detectable broadcast) between three parties, and also for solving the detectable liar detection problem. The protocol is suggested by the properties of a four-qubit entangled state, and the classical part of the protocol is simpler than that of previous proposals. In addition, we present an experimental implementation of the protocol using four-photon entanglement.

Figure 1

Quantum protocol for detectable Byzantine agreement. Three generals, $A$ (the commanding general), $B$, and $C$, are connected by pairwise authenticated error-free classical channels. In the first part of the protocol, four qubits prepared in the state $|{\Psi }^{(4)}⟩$ are distributed among the parties and, after a classical discussion, either (a) each general obtains a list $l_i$, or (b) all loyal generals agree to abort. If (a) then, in the second part of the protocol, $A$ sends $B$ ($C$) a message $m_{AB}$ ($m_{AC}$) and a list $l_{AB}$ ($l_{AC}$), and $B$ ($C$) sends $C$ ($B$) a message $m_{BC}$ ($m_{CB}$) and a list $l_{BC}$ ($l_{CB}$).

Figure 2

Scheme of the experimental setup. UV pulses pump a beta-barium borate crystal $BBO$. The degenerate down-conversion emission into the two directions, $a_0$ and $b_0$, is coupled into optical fibers by fiber couplers $FC$, then passes interference filters $F$. To generate the state $|{\Psi }^{(4)}⟩$, the initial emission modes are split with two nonpolarizing beam splitters $BS$. Two of the photons are sent to $A$, one to $B$, and one to $C$. Then, each party performs polarization measurements by inserting a half-wave plate $HWP$ and using a polarizing beam splitter $PBS$ and single-photon avalanche detectors.