  Trapped atomic ions are ideal single photon emitters with long lived internal
states which can be entangled with emitted photons. Coupling the ion to an
optical cavity enables efficient emission of single photons into a single
spatial mode and grants control over their temporal shape. These features are
key for quantum information processing and quantum communication. However, the
photons emitted by these systems are unsuitable for long-distance transmission
due to their wavelengths. Here we report the transmission of single photons
from a single $^{40}\text{Ca}^{+}$ ion coupled to an optical cavity over a 10
km optical fibre via frequency conversion from 866 nm to the telecom C-band at
1,530 nm. We observe non-classical photon statistics of the direct cavity
emission, the converted photons and the 10 km transmitted photons, as well as
the preservation of the photons' temporal shape throughout. This
telecommunication ready system can be a key component for long-distance quantum
communication as well as future cloud quantum computation.
