Coherence of Superpositions

Quantum coherence is important in quantum mechanics, and its essence is from superposition principle. We study the coherence of any two pure states and that of their arbitrary superposition, and obtain the relationship between them. In the case that the two states have support on orthogonal subspaces, the relationship is simple, that is, the difference between the coherence of their superposition state and the average coherence of them is smaller than 1. In other cases, we obtain different and a little more complicated relationships. Furthermore, we also obtain the lower bound of coherence of superpositions.