  The entanglement content of superpositions of quantum states is investigated
based on a measure called {\it concurrence}. Given a bipartite pure state in
arbitrary dimension written as the quantum superposition of two other such
states, we find simple inequalities relating the concurrence of the state to
that of its components. We derive an exact expression for the concurrence when
the component states are biorthogonal, and provide elegant upper and lower
bounds in all other cases. For quantum bits, our upper bound is tighter than
the previously derived bound in [Phys. Rev. Lett. 97, 100502 (2006).]
