Analytical bounds for decoy-state quantum key distribution with discrete phase randomization

TL;DR

This paper derives analytical bounds on the secret key rate for discrete phase randomized QKD protocols, simplifying security analysis and closely matching numerical results.

Contribution

It provides the first analytical bounds for DPR-based QKD protocols, reducing reliance on computationally intensive numerical optimizations.

Findings

Analytical bounds closely match numerical results in key regions.

Simplifies security analysis for DPR-based QKD protocols.

Enhances practical implementation by providing explicit bounds.

Abstract

We analyze the performance of quantum key distribution (QKD) protocols that rely on discrete phase randomization (DPR). For many QKD protocols that rely on weak coherent pulses (WCPs), continuous phase randomization is assumed, which simplifies the security proofs for such protocols. However, it is challenging to achieve such a perfect phase randomization in practice. As an alternative, we can select a discrete set of global phase values for WCPs, but we need to redo the security analysis for such a source. While security proofs incorporating DPR have been established for several QKD protocols, they often rely on computationally intensive numerical optimizations. To address this issue, in this study, we derive analytical bounds on the secret key generation rate of BB84 and measurement-device-independent QKD protocols in the DPR setting. Our analytical bounds closely match the results obtained from more cumbersome numerical methods in the regions of interest.