  When dealing with system-reservoir interactions in an open quantum system,
such as a photosynthetic light-harvesting complex, approximations are usually
made to obtain the dynamics of the system. One question immediately arises: how
good are these approximations, and in what ways can we evaluate them? Here, we
propose to use entanglement and a measure of non-Markovianity as benchmarks for
the deviation of approximate methods from exact results. We apply two
frequently-used perturbative but non-Markovian approximations to a
photosynthetic dimer model and compare their results with that of the
numerically-exact hierarchy equation of motion (HEOM). This enables us to
explore both entanglement and non-Markovianity measures as means to reveal how
the approximations either overestimate or underestimate memory effects and
quantum coherence. In addition, we show that both the approximate and exact
results suggest that non-Markonivity can, counter-intuitively, increase with
temperature, and with the coupling to the environment.
