  Entanglement distribution is at the heart of most quantum communication
protocols. Inevitable loss of photons along quantum channels is a major
obstacle for distributing entangled photons over long distances, as the
no-cloning theorem forbids the information to simply be amplified along the way
as is done in classical communication. It is therefore desirable for every
successfully transmitted photon pair to carry as much entanglement as possible.
Spontaneous parametric down-conversion (SPDC) creates photons entangled in
multiple high-dimensional degrees of freedom simultaneously, often referred to
as hyper-entanglement. In this work, we use a multicore fibre (MCF) to show
that energy-time and polarization degrees of freedom can simultaneously be
transmitted in multiple fibre cores, even maintaining path entanglement across
the cores. We verify a fidelity to the ideal Bell state of at least 95$\%$ in
all degrees of freedom. Furthermore, because the entangled photons are created
with a center wavelength of 1560 nm, our approach can readily be integrated
into modern telecommunication infrastructure, thus paving the way for high-rate
quantum key distribution and many other entanglement-based quantum
communication protocols.
