Finite-size quantum key distribution rates from R\'enyi entropies using conic optimization

Abstract:Finite-size general security proofs for quantum key distribution based on Rényi entropies have recently been introduced. These approaches are more flexible and provide tighter bounds on the secret key rate than traditional formulations based on the von Neumann entropy. However, deploying them requires minimizing the conditional Rényi entropy, a difficult optimization problem that has hitherto been tackled using ad-hoc techniques based on the Frank-Wolfe algorithm, which are unstable and can only handle particular cases. In this work, we introduce a method based on non-symmetric conic optimization for solving this problem. Our technique is fast, reliable, and completely general. We illustrate its performance on several protocols, whose results represent an improvement over the state of the art.

40 pages, 5 figures. v2: Added section 3.4 and extended Remark 1. v3: Added benchmarks. v4: Closer to the published version

arXiv:2511.10584 [quant-ph]

(or arXiv:2511.10584v4 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2511.10584 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1103/bf9s-m4jb Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.