LAUSR

Quantum coherence and entanglement are two key features in quantum mechanics and play important roles in quantum information processing and quantum computation. We provide a general triangle-like inequality satisfied by the $$l_1$$l1-norm measure of coherence for convex combination of arbitrary n pure states of a quantum state $$\rho $$ρ. Furthermore, we present triangle-like inequality for the convex-roof extended negativity for any states of rank 2, which gives a positive answer to a conjecture raised in Dai et al. (Phys. Rev. A 96:062308, 2017). Detailed examples are given to illustrate the relations characterized by the triangle-like inequalities.