Channel capacities quantify the optimal rates of sending information reliably
over noisy channels. Usually, the study of capacities assumes that the circuits
which sender and receiver use for encoding and decoding consist of perfectly
noiseless gates. In the case of communication over quantum channels, however,
this assumption is widely believed to be unrealistic, even in the long-term,
due to the fragility of quantum information, which is affected by the process
of decoherence. Christandl and M\”uller-Hermes have therefore initiated the
study of fault-tolerant channel coding for quantum channels, i.e. coding
schemes where encoder and decoder circuits are affected by noise, and have used
techniques from fault-tolerant quantum computing to establish coding theorems
for sending classical and quantum information in this scenario. Here, we extend
these methods to the case of entanglement-assisted communication, in particular
proving that the fault-tolerant capacity approaches the usual capacity when the
gate error approaches zero. A main tool, which might be of independent
interest, is the introduction of fault-tolerant entanglement distillation. We
furthermore focus on the modularity of the techniques used, so that they can be
easily adopted in other fault-tolerant communication scenarios.

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