Relations between coherence and path information

TL;DR

This paper explores the quantitative relationships between quantum coherence and path information in multi-path interferometers, extending previous two-path results using new coherence measures and entropic relations.

Contribution

It introduces two novel relations linking coherence and path information in multi-path interferometers, utilizing the $l_1$ measure and relative entropy-based measures.

Findings

Established a relation using $l_1$ coherence measure and visibility.

Derived an entropic relation involving mutual information and relative entropy coherence.

Extended two-path interferometer results to multi-path scenarios.

Abstract

We find two relations between coherence and path-information in a multi-path interferometer. The first builds on earlier results for the two-path interferometer, which used minimum-error state discrimination between detector states to provide the path information. For visibility, which was used in the two-path case, we substitute a recently defined $l_{1}$ measure of quantum coherence. The second is an entropic relation in which the path information is characterized by the mutual information between the detector states and the outcome of the measurement performed on them, and the coherence measure is one based on relative entropy.