Simple QKD keyrate computations from tangent-line bounds
Abstract
Recent work in quantum key distribution (QKD) has yielded finite-size keyrates based on convex optimisation problems, using the framework of entropy accumulation. Multiple solvers have been developed to address these optimisations in recent years, but have been based on a somewhat elaborate framework using sophisticated algorithms, in order to accommodate a broad range of QKD protocols. In this work, we note that for basic QKD protocols such as qubit BB84, the keyrates can be easily computed using off-the-shelf solvers instead, by obtaining suitable tangent lines to lower bound terms in the objective function. We compute the resulting finite-size keyrates and compare them to previous work. Moreover, we extend this approach to the six-state protocol, by deriving closed-form expressions for the single-round Rényi entropies in the protocol. This should facilitate subsequent study of the six-state protocol via entropy accumulation.
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BibTeX
@misc{goh2026simple,
title = {{Simple QKD keyrate computations from tangent-line bounds}},
author = {Jun Hui Goh and Ernest Y. -Z. Tan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09847},
eprint = {2609.09847},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09847},
}
RIS
TY - UNPB
TI - Simple QKD keyrate computations from tangent-line bounds
AU - Jun Hui Goh
AU - Ernest Y. -Z. Tan
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09847
UR - https://arxiv.org/abs/2609.09847
AB - Recent work in quantum key distribution (QKD) has yielded finite-size keyrates based on convex optimisation problems, using the framework of entropy accumulation. Multiple solvers have been developed to address these optimisations in recent years, but have been based on a somewhat elaborate framework using sophisticated algorithms, in order to accommodate a broad range of QKD protocols. In this work, we note that for basic QKD protocols such as qubit BB84, the keyrates can be easily computed using off-the-shelf solvers instead, by obtaining suitable tangent lines to lower bound terms in the objective function. We compute the resulting finite-size keyrates and compare them to previous work. Moreover, we extend this approach to the six-state protocol, by deriving closed-form expressions for the single-round Rényi entropies in the protocol. This should facilitate subsequent study of the six-state protocol via entropy accumulation.
ER -