Wave-particle duality in N-path interference

Bohr's principle of complementarity, in the context of a two-slit interference experiment, is understood as the quantitative measures of wave and particle natures following a duality relation D2+V2≤1. Here D is a measure of distinguishability of the two paths, and V is the visibility of interference. It is shown that such a relation can be formulated for N-slit or N-path interference too, with the proviso that the wave nature is characterized by a measure of coherence (C). This new relation, D2+C2≤1 is shown to be tight, and reduces to the known duality relation for the case N=2. A recently introduced similar relation (Bagan et al., 2016) is shown to be inadequate for the purpose.