# Advantage distillation for device-independent quantum key distribution

## TL;DR

This paper establishes a new security condition for advantage distillation in device-independent quantum key distribution, demonstrating it can tolerate higher noise and lower detector efficiency than previous methods, thus enhancing secure quantum communication.

## Contribution

It introduces a semidefinite programming approach to verify advantage distillation security conditions in DIQKD, surpassing existing noise and efficiency thresholds.

## Key findings

- Advantage distillation is secure up to 9.1% depolarising noise.
- Secure advantage distillation is possible with detector efficiencies as low as 89.1%.
- The method exceeds thresholds for one-way error correction using CHSH inequality.

## Abstract

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 $q \approx 9.1\%$ or limited detector efficiencies of $\eta \approx 89.1\%$ in a 2-input 2-output scenario. This exceeds the noise thresholds of $q \approx 7.1\%$ and $\eta \approx 90.7\%$ 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.