Abstract
The l1 norm of coherence and the relative entropy of coherence are the most general and easy to use quantifiers. Based on the l1 norm of coherence, we discuss the super-additivity inequalities and then give the explicit characterization of three-qubit pure states saturating these relations. We also prove that the l1 norm of coherence is super-additive for all pure states and qubit states. Further, we use the measure of the decay of quantum coherence to discuss how well ideal models of noise preserve the relative entropy of coherence on pure single-qubit sysrems.
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