Reply to “Comment on ‘Fully device-independent conference key agreement' ”

In this Reply we correct a mistake that we made in the correctness proofs of our protocol. Specifically, the Bell inequality we used ensures security but does not allow us to produce a key. In this Reply we explain and correct this mistake by adjusting the Bell inequality we used in the proof. Incidentally, this correction leads to slightly better asymptotic key rates. Importantly, none of the conclusions of the article are affected.

Figure 1

Asymptotic key rate for $N$-DICKA (dashed lines) and for the distribution of a secret key between $N$ parties through $(N-1)$- DIQKD protocols (solid lines), when each qubit experiences independent bit errors measured at a bit error rate (QBER) $Q$. For both types of protocols and from top to bottom, the lines correspond to the number of parties $N=\{3,4,5,6,7\}$. We observe that for the low-noise regime it is advantageous to use device-independent conference key agreement (DICKA) instead of $(N-1)\times \mathrm{DIQKD}$ (DIQKD = device-independent quantum key distribution). In general, the comparison between the two methods depends on the cost and noisiness of producing GHZ states over pairwise Einstein-Podolsky-Rosen pairs.