Adapting techniques from the field of information geometry, we show that open quantum system models of Frenkel exciton transport, a prevalent process in photosynthetic networks, belong to a class of mathematical models known as sloppy. Performing a Fisher-information-based multi-parameter sensitivity analysis to investigate the full dynamical evolution of the system and reveal this sloppiness, we establish which features of a transport network lie at the heart of efficient performance. We find that fine tuning the excitation energies in the network is generally far more important than optimizing the network geometry and that these conclusions hold for different measures of efficiency and when model parameters are subject to disorder within parameter regimes typical of molecular complexes involved in photosynthesis. Our approach and insights are equally applicable to other physical implementations of quantum transport.
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