  We find tight lower and upper bounds on the entanglement of a superposition
of two bipartite states in terms of the entanglement of the two states
constituting the superposition. Our upper bound is dramatically tighter than
the one presented in Phys. Rev. Lett 97, 100502 (2006) and our lower bound can
be used to provide lower bounds on different measures of entanglement such as
the entanglement of formation and the entanglement of subspaces. We also find
that in the case in which the two states are one-sided orthogonal, the
entanglement of the superposition state can be expressed explicitly in terms of
the entanglement of the two states in the superposition.
