Coherence of Superposition States**Supported by the National Natural Science Foundation of China under Grant Nos. 61671280, 11771009, and 11847101; by the Natural Science Basic Research Plan in Shaanxi Province of China under Grant No. 2017KJXX-92; by the Fundamental Research Funds for the Central Universities under Grant No. GK201902007 and by the Funded Projects for the Academic Leaders and Academic Backbones,

Abstract

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 l1-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.