Conversion of coherence into the generalized entanglement concurrence

We investigate the k-concurrence entanglement convertability theorem of coherence. By introducing the coherence number, which is the generalization of coherence rank to mixed states, we present a necessary and sufficient condition for a coherent mixed state to be converted to an entangled state of nonzero k-concurrence. We also quantitatively compare the amount of k-concurrence entanglement with coherence concurrence Cc, a recently introduced convex roof monotone of coherence.