Scalable implementation of $(d+1)$ mutually unbiased bases for $d$-dimensional quantum key distribution

TL;DR

This paper presents a scalable method to implement all $(d+1)$ mutually unbiased bases in high-dimensional quantum key distribution using a logarithmic number of interferometers, enhancing robustness and efficiency.

Contribution

It introduces a general, scalable implementation of $(d+1)$ MUBs for $d$-dimensional QKD using $ ext{log}_p d$ interferometers, applicable in prime power dimensions.

Findings

Achieved an average error rate of 3.8% for phase bases in $d=4$.

Demonstrated the setup's scalability and robustness against errors.

Lower error rate than the 23.17% threshold for secure QKD.

Abstract

A high-dimensional quantum key distribution (QKD) can improve error rate tolerance and the secret key rate. Many $d$-dimensional QKDs have used two mutually unbiased bases (MUBs), while $(d+1)$ MUBs enable a more robust QKD, especially against correlated errors. However, a scalable implementation has not been achieved because the setups have required $d$ devices even for two MUBs or a flexible convertor for a specific optical mode. Here, we propose a scalable and general implementation of $(d+1)$ MUBs using $\log_p d$ interferometers in prime power dimensions $d=p^N$. We implemented the setup for time-bin states and observed an average error rate of 3.8% for phase bases, which is lower than the 23.17% required for a secure QKD against coherent attack in $d=4$.