Device-independent secret key rates via a post-selected Bell inequality

TL;DR

This paper presents a novel device-independent quantum key distribution protocol that constructs optimal Bell inequalities from measurement data, enhancing security analysis and robustness across various scenarios.

Contribution

It introduces a general method to optimize Bell inequalities from data for DIQKD, applicable to any measurement settings and outcomes, with finite-size security analysis.

Findings

Achieves secure key rates with data-driven Bell inequalities

Demonstrates robustness across multiple Bell scenarios

Provides finite-size security analysis for collective attacks

Abstract

In device-independent quantum key distribution (DIQKD) the security is not based on any assumptions about the intrinsic properties of the devices and the quantum signals, but on the violation of a Bell inequality. We introduce a DIQKD scenario in which an optimal Bell inequality is constructed from the performed measurement data, rather than fixing beforehand a specific Bell inequality. Our method can be employed in a general way, for any number of measurement settings and any number of outcomes. We provide an implementable DIQKD protocol and perform finite-size security key analysis for collective attacks. We compare our approach with related procedures in the literature and analyze the robustness of our protocol. We also study the performance of our method in several Bell scenarios as well as for random measurement settings.