  Recent progress in resource theory of quantum coherence has resulted in
measures to quantify coherence in quantum systems. Especially, the l1-norm and
relative entropy of coherence have been shown to be proper quantifiers of
coherence and have been used to investigate coherence properties in different
operational tasks. Since long-lasting quantum coherence has been experimentally
confirmed in a number of photosynthetic complexes, it has been debated if and
how coherence is connected to the known efficiency of population transfer in
such systems. In this study, we investigate quantitatively the relationship
between coherence, as quantified by l1-norm and relative entropy of coherence,
and efficiency, as quantified by fidelity, for population transfer between
end-sites in a network of two-level quantum systems. In particular, we use the
coherence averaged over the duration of the population transfer in order to
carry out a quantitative comparision between coherence and fidelity. Our
results show that although coherence is a necessary requirement for population
transfer, there is no unique relation between coherence and the efficiency of
the transfer process.
