  The entanglement structure between different frequency components within
broadband quantum light pulses, forged at entanglement creation, represents a
promising route to the practical delivery of many multipartite quantum
information applications. However, the scalability of such applications is
largely limited by the entanglement decoherence caused by photon loss. One
promising method to combat such losses is noiseless linear amplification.
However, while there have been various procedures that implement noiseless
linear amplification on single-mode states, no realization has thus far been
proposed for noiseless linear amplification on quantum states carrying a
multimode structure. In this work we close this gap, proposing a novel
Noiseless Linear Amplifier (NLA) with Photon Catalysis (PC), namely, the
PC-NLA. Constructing a multimode version of an existing NLA that uses Quantum
Scissors (QS), the QS-NLA, we then show how the PC-NLA is compatible with the
QS-NLA, even though the former uses half the physical resources of the latter.
We then apply our newly developed multimode NLA frameworks to the problem of
Continuous-Variable (CV) entanglement distillation, determining how the
multimode structure of the entanglement impacts the performance of the NLAs.
Different from single-mode NLA analyses, we find that a multimode NLA is only
effective as a CV entanglement distillation strategy when the channel loss is
beyond some threshold - a threshold largely dependent on the multimode
structure. The results provided here will be valuable for real-world
implementations of multipartite quantum information applications that utilize
complex entanglement structure within broadband light pulses.
