Efficient Computation of QKD Key Rates without Semidefinite Programming
Abstract
Translating observed data into a reliable estimate of the secure key rate is a crucial step for operating a quantum key distribution device. We provide a computational method for this task that only requires eigenvalue computations and is therefore both fast and resource efficient. In contrast, existing approaches rely on semidefinite programming or programming on the entropy cone, whose memory requirements can scale as d4 in the underlying Hilbert-space dimension. Our method reduces this requirement to d2. A minimal implementation of our algorithm takes fewer than 100 lines of Common Lisp. We demonstrate real-time key-rate estimation on a Raspberry Pi with a 1 GB memory and a Cortex-A53 processor. Despite these modest resources, our implementation outperforms existing workstation-based benchmarks by several orders of magnitude. Non-numerical verification can be incorporated with little overhead using rational approximations. These results open the way toward embedding complete numerical security analysis directly into qkd hardware.
Related
- A variational quantum eigensolver-based cutting plane framework for semidefinite programming problems
- Multiplicative Semidefinite Programming Upper Bounds on Quantum No-Signalling-Assisted Zero-Error Capacity
- Efficient quantum Gibbs sampling of stabilizer codes using hybrid computation
- QUBO Sampling for Mixed Binary Quadratic Programming without Continuous Variable Binarization
- Efficient computation of the asymptotics of extensive-rank HCIZ integrals
BibTeX
@misc{temesi2026efficient,
title = {{Efficient Computation of QKD Key Rates without Semidefinite Programming}},
author = {Bence Temesi and Antoine Gansel and Gereon Koßmann and Rene Schwonnek},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.23285},
eprint = {2608.23285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23285},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Efficient Computation of QKD Key Rates without Semidefinite Programming
AU - Bence Temesi
AU - Antoine Gansel
AU - Gereon Koßmann
AU - Rene Schwonnek
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2608.23285
UR - https://arxiv.org/abs/2608.23285
AB - Translating observed data into a reliable estimate of the secure key rate is a crucial step for operating a quantum key distribution device. We provide a computational method for this task that only requires eigenvalue computations and is therefore both fast and resource efficient. In contrast, existing approaches rely on semidefinite programming or programming on the entropy cone, whose memory requirements can scale as d^4 in the underlying Hilbert-space dimension. Our method reduces this requirement to d^2. A minimal implementation of our algorithm takes fewer than 100 lines of Common Lisp. We demonstrate real-time key-rate estimation on a Raspberry Pi with a 1 GB memory and a Cortex-A53 processor. Despite these modest resources, our implementation outperforms existing workstation-based benchmarks by several orders of magnitude. Non-numerical verification can be incorporated with little overhead using rational approximations. These results open the way toward embedding complete numerical security analysis directly into qkd hardware.
ER -