Abstract
In this work, we evaluate quantum coherence using the $$l_{1}$$ -norm and convex-roof $$l_{1}$$ -norm and obtain several new results. First, we provide some new general triangle-like inequalities of quantum coherence, with results better than existing ones. Second, for some special three-dimensional quantum states, a method for calculating the convex-roof $$l_{1}$$ -norm is presented. Lastly, we offer distinct upper bounds in the $$l_{1}$$ -norm measure of coherence based on the quantum state itself.
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