Superadditivity relations of the l 1 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 l1 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 l1 norm of coherence. We show that the l1 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).