  Noiseless linear amplification (NLA) is useful for a wide variety of quantum
protocols. Here we propose a fully scalable amplifier which, for asymptotically
large sizes, can perform perfect fidelity NLA on any quantum state. Given
finite resources however, it is designed to perform perfect fidelity NLA on
coherent states and their arbitrary superpositions. Our scheme is a
generalisation of the multi-photon quantum scissor teleamplifier, which we
implement using a coherent state superposition resource state. Furthermore, we
prove our NLA is also a loss-tolerant relay for multi-ary phase-shift keyed
coherent states. Finally, we demonstrate that our NLA is also useful for
continuous-variable entanglement distillation, even with realistic experimental
imperfections.
