Finite-key analysis of loss-tolerant quantum key distribution based on random sampling theory

TL;DR

This paper introduces a new finite-key security analysis for loss-tolerant quantum key distribution protocols using random sampling theory, resulting in higher secret-key rates than previous Azuma's inequality-based methods.

Contribution

It presents an alternative security proof for LT QKD protocols based on random sampling theory, improving secret-key rate estimates over traditional Azuma's inequality methods.

Findings

Higher secret-key rates achieved with the new analysis.

Applicable to both prepare-and-measure and measurement-device-independent protocols.

Potential to extend to other QKD protocols using random sampling theory.

Abstract

The core of security proofs of quantum key distribution (QKD) is the estimation of a parameter that determines the amount of privacy amplification that the users need to apply in order to distill a secret key. To estimate this parameter using the observed data, one needs to apply concentration inequalities, such as random sampling theory or Azuma's inequality. The latter can be straightforwardly employed in a wider class of QKD protocols, including those that do not rely on mutually unbiased encoding bases, such as the loss-tolerant (LT) protocol. However, when applied to real-life finite-length QKD experiments, Azuma's inequality typically results in substantially lower secret-key rates. Here, we propose an alternative security analysis of the LT protocol against general attacks, for both its prepare-and-measure and measure-device-independent versions, that is based on random sampling theory. Consequently, our security proof provides considerably higher secret-key rates than the previous finite-key analysis based on Azuma's inequality. This work opens up the possibility of using random sampling theory to provide alternative security proofs for other QKD protocols.