  Spatial modes of light can potentially carry a vast amount of information,
making them promising candidates for both classical and quantum communication.
However, the distribution of such modes over large distances remains difficult.
Intermodal coupling complicates their use with common fibers, while free-space
transmission is thought to be strongly influenced by atmospheric turbulence.
Here we show the transmission of orbital angular momentum modes of light over a
distance of 143 kilometers between two Canary Islands, which is 50 times
greater than the maximum distance achieved previously. As a demonstration of
the transmission quality, we use superpositions of these modes to encode a
short message. At the receiver, an artificial neural network is used for
distinguishing between the different twisted light superpositions. The
algorithm is able to identify different mode superpositions with an accuracy of
more than 80% up to the third mode order, and decode the transmitted message
with an error rate of 8.33%. Using our data, we estimate that the distribution
of orbital angular momentum entanglement over more than 100 kilometers of free
space is feasible. Moreover, the quality of our free-space link can be further
improved by the use of state-of-the-art adaptive optics systems.
