Three-Slit Interference: A Duality Relation

TL;DR

This paper introduces a new duality relation for three-slit interference experiments, linking fringe visibility and path distinguishability using unambiguous quantum state discrimination, and extends the concept to two-slit interference.

Contribution

It proposes a novel path distinguishability measure based on UQSD and derives a tight inequality connecting interference visibility and which-way information for 3-slit experiments.

Findings

Derived a new duality inequality for 3-slit interference.

Introduced a path distinguishability measure based on UQSD.

Extended the duality relation to 2-slit interference, recovering known relations.

Abstract

The issue of interference and which-way information is addressed in the context of 3-slit interference experiments. A new path distinguishability ${\mathcal D_Q}$ is introduced, based on Unambiguous Quantum State Discrimination (UQSD). An inequality connecting the interference visibility and path distinguishability, ${\mathcal V} + {2{\mathcal D_Q}\over 3- {\mathcal D_Q}} \le 1$, is derived which puts a bound on how much fringe visibility and which-way information can be simultaneously obtained. It is argued that this bound is tight. For 2-slit interference, we derive a new duality relation which reduces to Englert's duality relation and Greenberger-Yasin's duality relation, in different limits.