Superadditivity relations of the l1 norm of coherence

Quantum coherence is an important physical resource in quantum computation and quantum information processing. Among the appropriate measures of quantum coherence, the l 1 norm of coherence is a widely known coherence measure and easy to use quantifiers. In this paper, we discuss the superadditivity inequalities and strong subadditivity of the l 1 norm of coherence. We show that the l 1 norm of coherence is superadditive for all states, which gives a positive answer to a conjecture in Liu and Li (Int J Theor Phys 56:494, 2017 ).