# Quantifying the Coherence Between Coherent States

## TL;DR

This paper introduces an orthogonalization method to quantify coherence in superpositions of coherent states, linking quantum coherence and nonclassicality through a resource theory framework.

## Contribution

It presents a novel orthogonalization procedure and a coherence monotone that connect quantum coherence with nonclassicality in quantum optics.

## Key findings

- The coherence measure characterizes nonclassicality via the Glauber-Sudarshan P distribution.
- The construction is part of a broader resource monotone framework in linear optics.
- Establishes connections between finite-dimensional coherence and continuous-variable nonclassicality.

## Abstract

In this paper, we detail an orthogonalization procedure that allows for the quantification of the amount of coherence present an arbitrary superposition of coherent states. The present construction is based on the quantum coherence resource theory introduced by Baumgratz et al., and the coherence resource monotone that we identify is found to characterize the nonclassicality traditionally analyzed via the Glauber-Sudarshan $P$ distribution. This suggests that identical quantum resources underlie both quantum coherence in the discrete finite dimensional case and the nonclassicality of quantum light. We show that our construction belongs to a family of resource monotones within the framework of a resource theory of linear optics, thus establishing deeper connections between the class of incoherent operations in the finite dimensional regime and linear optical operations in the continuous variable regime.