  We study the evolution of quantum entanglement during exciton energy transfer
(EET) in a network model of the Fenna-Matthews-Olson (FMO) complex, a
biological pigment-protein complex involved in the early steps of
photosynthesis in sulphur bacteria. The influence of Markovian, as well as
spatially and temporally correlated (non-Markovian) noise on the generation of
entanglement across distinct chromophores (site entanglement) and different
excitonic eigenstates (mode entanglement) is studied for different injection
mechanisms, including thermal and coherent laser excitation. Additionally, we
study the entangling power of the FMO complex under natural operating
conditions. While quantum information processing tends to favor maximal
entanglement, near unit EET is achieved as the result of an intricate interplay
between coherent and noisy processes where the initial part of the evolution
displays intermediate values of both forms of entanglement.
