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 $d=4$.

arXiv comment7 pages, 3 figures, followed by Supplemental Material of 11 pages, 2 figure, 2 table

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