  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 $d=4$.
