# Beating the repeaterless bound with adaptive measurement-device-independent quantum key distribution

## TL;DR

This paper analyzes the robustness of a quantum key distribution protocol that surpasses the repeaterless bound, focusing on the impact of source imperfections and identifying conditions sources must meet to maintain this advantage.

## Contribution

It derives necessary conditions on photon-number statistics for sources to beat the repeaterless bound and shows that certain practical sources like parametric down-conversion cannot achieve this.

## Key findings

- Parametric down-conversion sources do not meet the necessary conditions.
- The protocol's robustness depends on specific photon-number statistics.
- Idealized devices are required to surpass the repeaterless bound.

## Abstract

Surpassing the repeaterless bound is a crucial task on the way towards realizing long-distance quantum key distribution. In this paper, we focus on the protocol proposed by Azuma et al. in [Nature Communications 6, 10171 (2015)], which can beat this bound with idealized devices. We investigate the robustness of this protocol against imperfections in realistic setups, particularly the multiple-photon pair components emitted by practical entanglement sources. In doing so, we derive necessary conditions on the photon-number statistics of the sources in order to beat the repeaterless bound. We show, for instance, that parametric down-conversion sources do not satisfy the required conditions and thus cannot be used to outperform this bound.