# Experimental Test of Relation between Coherence and Path Information

## TL;DR

This paper experimentally investigates the duality relation between quantum coherence and path information using two-photon states, confirming theoretical predictions and enhancing understanding of wave-particle duality in quantum mechanics.

## Contribution

It provides the first experimental validation of the duality relation between quantum coherence and path information using the l1-norm measure and state discrimination techniques.

## Key findings

- Wave-particle complementarity and Bagan's equality are experimentally confirmed.
- The duality relation holds for the prepared two-photon states.
- Results offer insights into quantum coherence as a resource in quantum technologies.

## Abstract

Quantum coherence stemming from the superposition behaviour of a particle beyond the classical realm, serves as one of the most fundamental features in quantum mechanics. The wave-particle duality phenomenon, which shares the same origin, has a strong relationship with quantum coherence. Recently, an elegant relation between quantum coherence and path information has been theoretically derived. Here, we experimentally test such new duality by l1-norm measure and the minimum-error state discrimination. We prepare three classes of two-photon states encoded in polarisation degree of freedom, with one photon serving as the target and the other photon as the detector. We observe that wave-particle-like complementarity and Bagan's equality, defined by the duality relation between coherence and path information, is well satisfied. Our results may shed new light on the original nature of wave-particle duality and on the applications of quantum coherence as a fundamental resource in quantum technologies.