QKD parameter estimation by two-universal hashing

TL;DR

This paper introduces a new QKD protocol using two-universal hashing for error estimation, which significantly improves performance for small block sizes and reduces the gap between asymptotic and finite key rates.

Contribution

It proposes and proves the security of a novel QKD protocol that replaces random sampling with two-universal hashing for error estimation, enhancing efficiency for small block sizes.

Findings

Outperforms previous protocols for small block sizes

Finite key rate difference decreases as c/n with two-universal hashing

Compared to random sampling, the new protocol has a faster convergence rate

Abstract

This paper proposes and proves security of a QKD protocol which uses two-universal hashing instead of random sampling to estimate the number of bit flip and phase flip errors. This protocol dramatically outperforms previous QKD protocols for small block sizes. More generally, for the two-universal hashing QKD protocol, the difference between asymptotic and finite key rate decreases with the number $n$ of qubits as $cn^{-1}$, where $c$ depends on the security parameter. For comparison, the same difference decreases no faster than $c'n^{-1/3}$ for an optimized protocol that uses random sampling and has the same asymptotic rate, where $c'$ depends on the security parameter and the error rate.