# Generalized Coherence Concurrence and Path distinguishability

## TL;DR

This paper introduces a new family of coherence measures called generalized coherence concurrence, linking coherence to entanglement and applying it to multi-path interference to improve path distinguishability analysis.

## Contribution

It proposes the generalized coherence concurrence, connecting coherence monotones with entanglement, and applies it to enhance understanding of wave-particle duality in multi-path interference.

## Key findings

- Derived a sharper path distinguishability equation
- Linked coherence concurrence to the number of unambiguously identified slits
- Established a conversion criterion between coherence and entanglement

## Abstract

We propose a new family of coherence monotones, named the \emph{generalized coherence concurrence} (or coherence $k$-concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence $k$-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than $k$, and a state can be converted to a state with nonzero entanglement $k$-concurrence via incoherent operations if and only if the state has nonzero coherence $k$-concurrence. We apply the coherence concurrence family to the problem of wave-particle duality in multi-path interference phenomena. We obtain a sharper equation for path distinguishability (which witness the duality) than the known value and show that the amount of each concurrence for the quanton state determines the number of slits which are identified unambiguously.