# Improving parameter estimation of entropic uncertainty relation in continuous-variable quantum key distribution

## TL;DR

This paper enhances parameter estimation in the entropic uncertainty relation for continuous-variable quantum key distribution by addressing finite-size effects and introducing a double-data modulation method, leading to improved security and efficiency.

## Contribution

It introduces an adapted parameter estimation technique considering finite-size effects and employs double-data modulation to improve key efficiency in EUR-based quantum key distribution.

## Key findings

- Effective parameter estimation under finite-size effects
- Double-data modulation reduces key consumption
- Improved practical performance of EUR in quantum key distribution

## Abstract

The entropic uncertainty relation (EUR) is of significant importance in the security proof of continuous-variable quantum key distribution under coherent attacks. The parameter estimation in the EUR method contains the estimation of the covariance matrix (CM), as well as the max-entropy. The discussions in previous works have not involved the effect of finite-size on estimating the CM, which will further affect the estimation of leakage information. In this work, we address this issue by adapting the parameter estimation technique to the EUR analysis method under composable security frameworks. We also use the double-data modulation method to improve the parameter estimation step, where all the states can be exploited for both parameter estimation and key generation; thus, the statistical fluctuation of estimating the max-entropy disappears. The result shows that the adapted method can effectively estimate parameters in EUR analysis. Moreover, the double-data modulation method can, to a large extent, save the key consumption, which further improves the performance in practical implementations of the EUR.