Advantage Distillation for Device-Independent Quantum Key Distribution

Device-independent quantum key distribution (DIQKD) offers the prospect of distributing secret keys with only minimal security assumptions, by making use of a Bell violation. However, existing DIQKD security proofs have low noise tolerances, making a proof-of-principle demonstration currently infeasible. We investigate whether the noise tolerance can be improved by using advantage distillation, which refers to using two-way communication instead of the one-way error correction currently used in DIQKD security proofs. We derive an efficiently verifiable condition to certify that advantage distillation is secure against collective attacks in a variety of DIQKD scenarios, and use this to show that it can indeed allow higher noise tolerances, which could help to pave the way towards an experimental implementation of DIQKD.

Figure 1

Left- and right-hand sides of Eq. (6), shown as solid and dashed curves, respectively, for a DIQKD scenario where the target distribution attains maximum CHSH violation in the absence of noise. Plot (a) shows the effect of depolarizing noise $q$, while in plot (b) a small amount of depolarizing noise is applied ($q=0.1\%$ for the black curve, $q=1\%$ for the blue curve) followed by a limited-detection-efficiency noise model with efficiency $\eta$. In plots (a) and (b), the solid and dashed curves intersect at $q_t\approx 7.7\%$ and ${\eta }_t\approx 91.7\%$ (black), 92.6% (blue), respectively, which yield the threshold values such that we can show positive key rate is achievable via Corollary 1. The solid curves reach zero at the same noise values as where the CHSH violation becomes zero.