Trends in photonic quantum information follow closely the technical progress in classical optics and telecommunications. In this regard, advances in multiplexing optical communications channels have also been pursued for the generation of multi-dimensional quantum states (qudits), since their use is advantageous for several quantum information tasks. One current path leading in this direction is through the use of space-division multiplexing multi-core optical fibers, which provides a new platform for efficiently controlling path-encoded qudit states. Here we report on a parametric down-conversion source of entangled qudits that is fully based on (and therefore compatible with) state-of-the-art multi-core fiber technology. The source design uses modern multi-core fiber beam splitters to prepare the pump laser beam as well as measure the generated entangled state, achieving high spectral brightness while providing a stable architecture. In addition, it can be readily used with any core geometry, which is crucial since widespread standards for multi-core fibers in telecommunications have yet to be established. Our source represents an important step towards the compatibility of quantum communications with the next-generation optical networks.