Abstract
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).
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