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 ${ \mathcal D}^2+{ \mathcal V}^2 \le 1$. Here ${ \mathcal D}$ is a measure of distinguishability of the two paths, and ${ \mathcal V}$ 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 { \em coherence} (${ \mathcal C}$). This new relation, ${ \mathcal D}^2+{ \mathcal C}^2 \le 1$ 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.
Categories: quant-ph