Numerical Security Proof for Decoy-State BB84 and Measurement-Device-Independent QKD Resistant against Large Basis Misalignment

TL;DR

This paper introduces a numerical framework incorporating decoy-state analysis and fine-grained statistics to enhance the robustness and key rate of BB84 and MDI-QKD protocols against basis misalignments.

Contribution

It develops a numerical method that integrates decoy-state analysis with fine-grained statistics, improving QKD performance under misalignment conditions.

Findings

Enhanced key rates with misalignment resilience

Extended maximum transmission distance for protocols

Reduced need for manual basis alignment

Abstract

In this work, we incorporate decoy-state analysis into a well-established numerical framework for key rate calculation, and apply the numerical framework to decoy-state BB84 and measurement-device-independent (MDI) QKD protocols as examples. Additionally, we combine with these decoy-state protocols what is called "fine-grained statistics", which is a variation of existing QKD protocols that makes use of originally discarded data to get a better key rate. We show that such variations can grant protocols resilience against any unknown and slowly changing rotation along one axis, similar to reference-frame-independent QKD, but without the need for encoding physically in an additional rotation-invariant basis. Such an analysis can easily be applied to existing systems, or even data already recorded in previous experiments, to gain significantly higher key rate when considerable misalignment is present, extending the maximum distance for BB84 and MDI-QKD and reducing the need for manual alignment in an experiment.