In this thesis, we are interested in the limits of quantum communication with and without entanglement, and with and without noise assumptions on the communication setup. When a sender and a receiver are connected by a communication line that is governed by noise which is modelled by a quantum channel, they hope to design a coding scheme, i.e. messages and message decoders, in such a way that they are robust to this noise. The amount of message bits per channel use is called the achievable rate of the coding scheme, and the maximal achievable rate for a given quantum channel is called capacity of the quantum channel. Here, we are interested in coding schemes and capacities under various assumptions, in particular in the case where the sender and the receiver share quantum entanglement, which turns out to be the most natural generalization of the classical communication analogue that lies at the basis of many of our modern technologies.

In order to communicate with a quantum computer, the encoding and decoding of a message for a quantum channel on a quantum computer is implemented by a sequence of gates from a finite gate set. For classical channels, these gates are assumed to be noise-free at the timescales relevant for communication, but this assumption is likely not justified for quantum circuits. In the first part of this thesis, we show that the encoding and decoding for entanglement-assisted communication can be protected against noise by the use of techniques from quantum fault-tolerance and error correction without significantly decreasing the capacity. In particular, we recover the usual, noiseless case as the probability of errors in the circuit approaches zero.

In the second part, we study a proposal for fault-tolerance on trapped ion quantum devices in order to gauge their potential for implementing communication protocols and to assess our assumptions about noise models, with a particular focus on the preparation of maximally entangled states.

In the final part of the thesis, we revisit the comparison between quantum communication setups where the sender and the receiver have access to entanglement and setups where they do not. It is well-known that the communication rates are improved when entanglement is present. Here, we show that this improvement can be bounded for a large class of finite dimensional channels, taking a step towards resolving a conjecture from one of the earliest papers on entanglement-assisted communication.