# Practical issues in decoy-state quantum key distribution based on the central limit theorem

## TL;DR

This paper proposes a decoy-state statistical analysis method for quantum key distribution based on the central limit theorem, addressing finite-key effects and practical implementation issues.

## Contribution

It introduces a new statistical processing approach for decoy states in QKD using the central limit theorem, improving estimation accuracy.

## Key findings

- Estimations are tight and reliable.
- Method accounts for statistical fluctuations and failure probabilities.
- Suitable for industrial QKD systems.

## Abstract

Decoy-state quantum key distribution is a standard tool for long-distance quantum communications. An important issue in this field is processing the decoy-state statistics taking into account statistical fluctuations (or "finite-key effects"). In this work, we propose and analyze an option for decoy statistics processing, which is based on the central limit theorem. We discuss such practical issues as an inclusion of the failure probability of the decoy-states statistical estimates in the total failure probability of a QKD protocol and also taking into account the deviations of the binomially distributed random variables used in the estimations from the Gaussian distribution. The results of numerical simulations show that the obtained estimations are quite tight. The proposed technique can be used as a part of post-processing procedures for industrial quantum key distribution systems.