Generalized Coherence Concurrence and Path distinguishability

We propose a new family of coherence monotones, named the generalized coherence concurrence (or coherence k-concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence k-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than k, and a state can be converted to a state with nonzero entanglement k-concurrence via incoherent operations if and only if the state has nonzero coherence k-concurrence. The generalized coherence concurrence can be considered as the entanglement-based coherence monotone. We also compare the second member of the monotone family with other known monotones and obtain an inequality which reinforces the assumption that l1-norm monotone in coherence is analogous to negativity in entanglement. PACS numbers: 03.67.a, 03.65.Ud