  In the device-independent quantum information approach, the implementation of
a given task can be self-tested solely from the recorded statistics and without
detailed models for the employed devices. Even though experimentally demanding,
it provides appealing verification schemes for advanced quantum technologies
that naturally fulfil the associated requirements. In this work, we
experimentally study whether self-testing protocols can be adopted to certify
the proper functioning of new quantum devices built with modern space-division
multiplexing optical fiber technology. Specifically, we consider the
prepare-and-measure protocol of M.~Farkas and J.~Kaniewski (Phys.~Rev.~A 99,
032316) for self-testing measurements corresponding to mutually unbiased bases
(MUBs) in a dimension $d>2$. In our scheme, the state preparation and
measurement stages are implemented with a multi-arm interferometer built with
new multi-core optical fibers and related components. Due to the high-overlap
of the interferometer's optical modes achieved with this technology, we are
able to reach the required visibilities for self-testing the implementation of
two four-dimensional MUBs. We also quantify two operational quantities of the
measurements: (i) the incompatibility robustness, connected to Bell violations,
and (ii) the randomness extractable from the outcomes. Since MUBs lie at the
core of several quantum information protocols, our results are of practical
interest for future quantum works relying on space-division multiplexing
optical fibers.
