Higher-order wave-particle duality

Abstract

The complementarity of a single photon's particlelike and wavelike behaviors can be described by the inequality ${D}^{2}+{V}^{2}\ensuremath{\le}1$, with $D$ being the path distinguishability and $V$ being the fringe visibility. In this paper, we generalize this duality relation to the multiphoton case, where two concepts, higher-order distinguishability and higher-order fringe visibility, are introduced to quantify the higher-order particlelike and wavelike behaviors of multiphotons.