$l_1$-norm coherence of assistance

We introduce and study the $l_1$-norm coherence of assistance both theoretically and operationally. We first provide an upper bound for the $l_1$-norm coherence of assistance and show a necessary and sufficient condition for the saturation of the upper bound. For two- and three-dimensional quantum states, the analytical expression of the $l_1$-norm coherence of assistance is given. Operationally, the mixed quantum coherence can always be increased with the help of another party's local measurement and one way classical communication since the $l_1$-norm coherence of assistance, as well as the relative-entropy coherence of assistance, are shown to be strictly larger than the original coherence. The relation between the $l_1$-norm coherence of assistance and entanglement is revealed. Finally, a comparison between the $l_1$-norm coherence of assistance and the relative-entropy coherence of assistance is made.