Entropic framework for wave-particle duality in multipath interferometers

TL;DR

This paper extends the unification of wave-particle duality relations and the uncertainty principle to n-path interferometers using an entropic framework, deriving new inequalities for complex quantum systems.

Contribution

It generalizes the unification of wave-particle duality and uncertainty principles to multi-path interferometers with a novel entropic approach.

Findings

Derived new wave-particle duality relations for n-path interferometers.

Unified duality relations with entropy-based uncertainty principles.

Provided a framework for universally valid WPDRs in complex interferometers.

Abstract

An interferometer - no matter how clever the design - cannot reveal both the wave and particle behavior of a quantum system. This fundamental idea has been captured by inequalities, so-called wave-particle duality relations (WPDRs), that upper bound the sum of the fringe visibility (wave behavior) and path distinguishability (particle behavior). Another fundamental idea is Heisenberg's uncertainty principle, stating that some pairs of observables cannot be known simultaneously. Recent work has unified these two principles for two-path interferometers. Here we extend this unification to $n$-path interferometers, showing that WPDRs correspond to a modern formulation of the uncertainty principle stated in terms of entropies. Furthermore, our unification provides a framework for solving an outstanding problem of how to formulate universally valid WPDRs for interferometers with more than two paths, and we employ this framework to derive some novel WPDRs.