  We find two relations between coherence and path-information in a multi-path
interferometer. The first builds on earlier results for the two-path
interferometer, which used minimum-error state discrimination between detector
states to provide the path information. For visibility, which was used in the
two-path case, we substitute a recently defined $l_{1}$ measure of quantum
coherence. The second is an entropic relation in which the path information is
characterized by the mutual information between the detector states and the
outcome of the measurement performed on them, and the coherence measure is one
based on relative entropy.
