High-dimensional quantum key distribution rates for multiple measurement bases

TL;DR

This paper explores how high-dimensional encoding and multiple measurement bases can enhance quantum key distribution rates, analyzing asymptotic and finite-key scenarios with various numbers of mutually unbiased bases.

Contribution

It provides an analytic expression for the key rate with multiple MUBs and optimizes finite key rates considering different attack models and measurement bases.

Findings

Using three MUBs yields higher key rates in small round scenarios.

The key rate depends on the number of MUBs and system dimension.

Optimal number of MUBs varies between asymptotic and finite regimes.

Abstract

We investigate the advantages of high-dimensional encoding for a quantum key distribution protocol. In particular, we address a BBM92-like protocol where the dimension of the systems can be larger than two and more than two mutually unbiased bases (MUBs) can be employed. Indeed, it is known that, for a system whose dimension $d$ is a prime or the power of a prime, up to $d+1$ MUBs can be found. We derive an analytic expression for the asymptotic key rate when $d+1$ MUBs are exploited and show the effects of using different numbers of MUBs on the performance of the protocol. Then, we move to the non-asymptotic case and optimize the finite key rate against collective and coherent attacks for generic dimension of the systems and all possible numbers of MUBs. In the finite-key scenario, we find that, if the number of rounds is small enough, the highest key rate is obtained by exploiting three MUBs, instead of $d+1$ as one may expect.