Title: Generalized Coherence Concurrence and Path distinguishability,
Abstract: We propose a new family of coherence monotones, named the \emph{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. We apply the coherence concurrence family to the
problem of wave-particle duality in multi-path interference phenomena. We
obtain a sharper equation for path distinguishability (which witness the
duality) than the known value and show that the amount of each concurrence for
the quanton state determines the number of slits which are identified
unambiguously.