  When shared between remote locations, entanglement opens up fundamentally new
capabilities for science and technology [1, 2]. Envisioned quantum networks
distribute entanglement between their remote matter-based quantum nodes, in
which it is stored, processed and used [1]. Pioneering experiments have shown
how photons can distribute entanglement between single ions or single atoms a
few ten meters apart [3, 4] and between two nitrogen-vacancy centres 1 km apart
[5]. Here we report on the observation of entanglement between matter (a
trapped ion) and light (a photon) over 50~km of optical fibre: a practical
distance to start building large-scale quantum networks. Our methods include an
efficient source of light-matter entanglement via cavity-QED techniques and a
quantum photon converter to the 1550~nm telecom C band. Our methods provide a
direct path to entangling remote registers of quantum-logic capable trapped-ion
qubits [6 - 8], and the optical atomic clock transitions that they contain [9,
10], spaced by hundreds of kilometers.
