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We introduce and study the l1 norm of coherence of assistance boththeoretically and operationally. We first provide an upper bound for the l1norm of coherence of assistance and show a necessary and sufficient conditionfor the saturation of the upper bound. For two and three dimensional quantumstates, the analytical expression of the l1 norm of coherence of assistance isgiven. Operationally, the mixed quantum coherence can always be increased withthe help of another party' s local measurement and one way classicalcommunication since the l1 norm of coherence of assistance, as well as therelative entropy of coherence of assistance, is shown to be strictly largerthan the original coherence. The relation between the l1 norm of coherence ofassistance and entanglement is revealed. Finally, a comparison between the l1norm of coherence of assistance and the relative entropy of coherence ofassistance is made.

The l1 Norm of Coherence of Assistance