Wave Particle Duality in Asymmetric Beam Interference

TL;DR

This paper derives new duality relations for asymmetric two-slit interference experiments, clarifying the conditions under which wave-particle duality manifests when paths are unequally probable or slit widths differ.

Contribution

It introduces generalized duality relations for asymmetric beam interference, extending previous symmetric case results and clarifying the meaning of path information.

Findings

Derived duality inequalities for asymmetric paths

Duality relations saturate for pure states

Recovers earlier results in special cases

Abstract

It is well known that in a two-slit interference experiment, acquiring which-path information about the particle, leads to a degrading of the interference. It is argued that path-information has a meaning only when one can umabiguously tell which slit the particle went through. Using this idea, two duality relations are derived for the general case where the two paths may not be equally probable, and the two slits may be of unequal widths. These duality relations, which are inequalities in general, saturate for all pure states. Earlier known results are recovered in suitable limit.