  Multi-port beamsplitters are cornerstone devices for high-dimensional quantum
information tasks, which can outperform the two-dimensional ones. Nonetheless,
the fabrication of such devices has been proven to be challenging with progress
only recently achieved with the advent of integrated photonics. Here, we report
on the production of high-quality $N \times N$ (with $N=4,7$) multi-port
beamsplitters based on a new scheme for manipulating multi-core optical fibers.
By exploring their compatibility with optical fiber components, we create
4-dimensional quantum systems and implement the measurement-device-independent
random number generation task with a programmable 4-arm interferometer
operating at a 2 MHz repetition rate. Thanks to the high visibilities observed,
we surpass the 1-bit limit of binary protocols and attain 1.23 bits of
certified private randomness per experimental round. Our result demonstrates
that fast switching, low-loss and high optical quality for high-dimensional
quantum information can be simultaneously achieved with multi-core fiber
technology.
