Finite-key security analysis for multilevel quantum key distribution

TL;DR

This paper provides a comprehensive security analysis of d-dimensional quantum key distribution protocols using multiple mutually unbiased bases, highlighting their advantages over BB84 and discussing potential experimental implementations.

Contribution

It extends finite key security analysis to d-level MUB QKD protocols and generalizes uncertainty relations for these systems.

Findings

Finite key rates increase with dimension d and number of MUBs.

Protocols potentially outperform BB84 in key rate and security thresholds.

Discussion of experimental realization using photon orbital angular momentum.

Abstract

We present a detailed security analysis of a d-dimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finite key length scenario. The finite secret key rates are calculated as a function of the length of the sifted key by (i) generalizing the uncertainly relation-based insight from BB84 to any d-level 2-MUB QKD protocol and (ii) by adopting recent advances in the second-order asymptotics for finite block length quantum coding (for both d-level 2- and 3-MUB QKD protocols). Since the finite and asymptotic secret key rates increase with d and the number of MUBs (together with the tolerable threshold) such QKD schemes could in principle offer an important advantage over BB84. We discuss the possibility of an experimental realization of the 3-MUB QKD protocol with the orbital angular momentum degrees of freedom of photons.