Interference Visibility and Wave-Particle Duality in Multi-Path Interference

Wave-particle duality in multi-path interference is fraught with issues despite substantial progress in recent years. It was experimentally shown that in certain specific conditions, getting path information in a multi-path experiment can actually increase the visibility of interference. As a result, it was argued that in multi-path interference experiments, visibility of interference and 'which-path' information are not always complementary observables. In the present work, a new wave-particle duality relation is presented, based on a sum of visibilities of interference from individual pairs of path. This relation is always respected, even in the kind of specific situations mentioned above. This sum of visibilities turns out to be related to a recently introduced measure of coherence. As one of the consequences, it provides a novel way of experimentally measuring coherence in a multi-path interference experiment. As another consequence, this relation suggests a simple way of measuring path-distinguishability in multi-path interference. In addition, it resolves several outstanding issues concerning wave-particle duality in multi-path interference.