  We study the properties of coherence concurrence and present a physical
explanation analogous to the coherence of assistance. We give an optimal pure
state decomposition which attains the coherence concurrence for qubit states.
We prove the additivity of coherence concurrence under direct sum operations in
another way. Using these results, we calculate analytically the coherence
concurrence for X states and show its optimal decompositions. Moreover, we show
that the coherence concurrence is exactly twice the convex roof extended
negativity of the Schmidt correlated states, thus establishing a direct
relation between coherence concurrence and quantum entanglement.
