Improved DIQKD protocols with finite-size analysis

TL;DR

This paper presents a comprehensive finite-size security proof for advanced DIQKD protocols, achieving higher noise thresholds and improved key rates through novel analysis and protocol modifications.

Contribution

It introduces a general finite-size security proof applicable to recent DIQKD improvements, with tighter bounds and higher noise tolerance.

Findings

Achieves positive key rates up to 9.33% depolarizing noise

Develops a method for tight lower bounds on asymptotic keyrate

Enhances key rates by modifying random-key-measurement protocols

Abstract

The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on noisy preprocessing, random key measurements, and modified CHSH inequalities. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of $9.33\%$, exceeding all previously known noise thresholds. We also develop a modification to random-key-measurement protocols, using a pre-shared seed followed by a "seed recovery" step, which yields substantially higher net key generation rates by essentially removing the sifting factor. Some of our results may also improve the keyrates of device-independent randomness expansion.