  Quantum tunneling events occurring through biochemical bonds are capable to
generate quantum correlations between bonded systems, which in turn makes the
conventional second law of thermodynamics approach insufficient to investigate
these systems. This means that the utilization of these correlations in their
biological functions could give an evolutionary advantage to biomolecules to an
extent beyond the predictions of molecular biology that are generally based on
the second law in its standard form. To explore this possibility, we first
compare the tunneling assisted quantum entanglement shared in the ground states
of covalent and hydrogen bonds. Only the latter appears to be useful from a
quantum information point of view. Also, significant amounts of quantum
entanglement can be found in the thermal state of hydrogen bond. Then, we focus
on an illustrative example of ligand binding in which a receptor protein or an
enzyme is restricted to recognize its ligands using the same set of
proton-acceptors and donors residing on its binding site. In particular, we
show that such a biomolecule can discriminate between $3^n - 1$ agonist ligands
if it uses the entanglement shared in $n$ intermolecular hydrogen bonds as a
resource in molecular recognition. Finally, we consider the molecular
recognition events encountered in both the contemporary genetic machinery and
its hypothetical primordial ancestor in pre-DNA world, and discuss whether
there may have been a place for the utilization of quantum entanglement in the
evolutionary history of this system.
