We derive a sufficient condition for advantage distillation to be secure against collective attacks in device-independent quantum key distribution (DIQKD), focusing on the repetition-code protocol. In addition, we describe a semidefinite programming method to check whether this condition holds for any probability distribution obtained in a DIQKD protocol. Applying our method to various probability distributions, we find that advantage distillation is possible up to depolarising-noise values of q≈9.1% or limited detector efficiencies of η≈89.1% in a 2-input 2-output scenario. This exceeds the noise thresholds of q≈7.1% and η≈90.7% respectively for DIQKD with one-way error correction using the CHSH inequality, thereby showing that it is possible to distill secret key beyond those thresholds.
@article{arxiv.1903.10535,
title = {Advantage distillation for device-independent quantum key distribution},
author = {Ernest Y. -Z. Tan and Charles C. -W. Lim and Renato Renner},
journal= {arXiv preprint arXiv:1903.10535},
year = {2020}
}
Comments
[v2] Corrected threshold detection efficiency for one-way error correction, reorganised material. [v3] Updated funding information