# Information-theoretic security proof of differential-phase-shift quantum key distribution protocol based on complementarity

## TL;DR

This paper presents an information-theoretic security proof for the differential-phase-shift quantum key distribution protocol using the complementarity approach, resulting in improved key rates and broader applicability compared to previous methods.

## Contribution

It introduces a security proof based on the complementarity approach that enhances key rate estimation and removes the need for numerical calculations, enabling security evaluation for any block size.

## Key findings

- Achieved slightly better key generation rate than previous proofs.
- Eliminated the need for numerical calculations in security estimation.
- Enabled security evaluation for any block size.

## Abstract

We show the information-theoretic security proof of the differential-phase-shift (DPS) quantum key distribution (QKD) protocol based on the complementarity approach [arXiv:0704.3661 (2007)]. Our security proof provides a slightly better key generation rate compared to the one derived in the previous security proof in [arXiv:1208.1995 (2012)] that is based on the Shor-Preskill approach [Phys. Rev. Lett. ${\bf 85}$, 441 (2000)]. This improvement is obtained because the complementarity approach can employ more detailed information on Alice's sending state in estimating the leaked information to an eavesdropper. Moreover, we remove the necessity of the numerical calculation that was needed in the previous analysis to estimate the leaked information. This leads to an advantage that our security proof enables us to evaluate the security of the DPS protocol with any block size. This paper highlights one of the fundamental differences between the Shor-Preskill and the complementarity approaches.