The key task of transmitting quantum states encompasses a diverse array of tech- niques and applications. This thesis presents experimental work in optical quantum information science, focused on strategies for transmitting quantum states with high fidelity and security. The majority of the work in this thesis is in photonic quantum information science, although one experiment used continuous–variable states. In the first experiment, the noiseless amplification of a photon polarisation qubit was realised, using delocalised single photon ancilla states and two single–mode amplification stages operating coherently. Artificial loss was applied to a single photon, to simulate a loss in a long–distance quantum transmission channel, and for the highest gain setting that was investigated, the qubit amplifier achieved a five–fold increase in transmission fidelity. In the second experiment, linear optical techniques for distributing mode entangle- ment in a quantum network were studied. Quantum networks are based on a series of nodes, potentially separated by significant distances, and connected via quantum repeaters. Different quantum repeater architectures have been proposed, but they all include embedded distillation stages, which are based on linear optical techniques. We simulate two distinct quantum repeater scenarios, using different configurations of an entanglement swapping stage, a noiseless single–mode amplification stage, and loss. The performance of the amplification stage in overcoming the loss is characterised in both configurations. Significant distillation of mode entanglement is achieved in one configuration, and an increase in mode coherence is achieved in the other configuration.