Hierarchy of inequalities for quantitative duality

TL;DR

This paper establishes a hierarchy of inequalities in two-way interferometry that relate fringe visibility and which-way information, revealing how different sources of information influence quantum duality.

Contribution

It introduces a hierarchy of duality inequalities that account for multiple sources of which-way information, extending previous bounds to mixed states and unbalanced interferometers.

Findings

Derived a hierarchy of duality inequalities

Established a more stringent inequality for mixed states

Linked fringe visibility to multiple sources of which-way information

Abstract

We derive different relations quantifying duality in a generic two-way interferometer. These relations set different upper bounds to the visibility V of the fringes measured at the output port of the interferometer. A hierarchy of inequalities is presented which exhibits the influence of the availability to the experimenter of different sources of which-way information contributing to the total distinguishability D of the ways. For mixed states and unbalanced interferometers an inequality is derived, V^2+ Xi^2 \leq 1, which can be more stringent than the one associated with the distinguishability (V^2+ D^2 \leq 1).