Coherence of Superposition States*

We find tight upper bound on the coherence of a superposition of two states in terms of the coherence of the two states constituting the superposition with $l_{1}$-norm of coherence. Our upper bound is tighter than the one presented by Liu, et al. [Quantum Inf. Process. 15 (2016) 4209.] We also generalize the results to the case that the superposition is constituted with more than two states in high dimension, and we give the corresponding upper bounds.