  It is shown that, if the loss of entanglement along a quantum channel is
sufficiently small, then approximate quantum error correction is possible,
thereby generalizing what happens for coherent information. Explicit bounds are
obtained for the entanglement of formation and the distillable entanglement,
and their validity naturally extends to other bipartite entanglement measures
in between. Robustness of derived criteria is analyzed and their tightness
compared. Finally, as a byproduct, we prove a bound quantifying how large the
gap between entanglement of formation and distillable entanglement can be for
any given finite dimensional bipartite system, thus providing a sufficient
condition for distillability in terms of entanglement of formation.
