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

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.