  We revisit critically the recent claims, inspired by quantum optics and
quantum information, that there is entanglement in the biological pigment
protein complexes, and that it is responsible for the high transport
efficiency. While unexpectedly long coherence times were experimentally
demonstrated, the existence of entanglement is, at the moment, a purely
theoretical conjecture; it is this conjecture that we analyze. As demonstrated
by a toy model, a similar transport phenomenology can be obtained without
generating entanglement. Furthermore, we also argue that even if entanglement
does exist, it is purely incidental and seems to plays no essential role for
the transport efficiency. We emphasize that our paper is not a proof that
entanglement does not exist in light-harvesting complexes - this would require
a knowledge of the system and its parameters well beyond the state of the art.
Rather, we present a counter-example to the recent claims of entanglement,
showing that the arguments, as they stand at the moment, are not sufficiently
justified and hence cannot be taken as proof for the existence of entanglement,
let alone of its essential role, in the excitation transport.
