Wave-Particle Duality in N-Path Interference

TL;DR

This paper generalizes the wave-particle duality relation from two-slit to N-path interference, introducing a coherence-based measure for wave nature and demonstrating the relation's tightness and consistency with known cases.

Contribution

It formulates a new duality relation for N-path interference using coherence, extending the wave-particle duality concept beyond two-slit experiments.

Findings

The new relation ${ ext{D}}^2 + { ext{C}}^2 \, \le \, 1$ is tight and valid for N-path interference.

Reduces to the known duality relation when N=2.

Shows inadequacy of a recent similar relation by Bagan et al. (2016).

Abstract

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.