Coherence concurrence for X states

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 pure state 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.