# Entanglement of Identical Particles and Coherence in the First Quantization Language

## TL;DR

This paper introduces a formalism in the first quantization language to analyze entanglement and coherence of identical particles, enabling the use of standard quantum information tools for these systems.

## Contribution

It develops a new formalism that connects entanglement and coherence in identical particles using first quantization, extending existing detection protocols.

## Key findings

- Quantitative relation between entanglement and spatial coherence.
- Generalized entanglement detection process for identical particles.
- Application of quantum information tools to indistinguishable particles.

## Abstract

We suggest a formalism to illustrate the entanglement of identical particles in the first quantization language (1QL). Our 1QL formalism enables one to exploit all the well-established quantum information tools to understand the indistinguishable ones, including the reduced density matrix and familiar entanglement measures. The rigorous quantitative relation between the amount of entanglement and the spatial coherence of particles is possible in this formalism. Our entanglement detection process is a generalization of the entanglement extraction protocol for identical particles with mode splitting proposed by Killoran et al. (2014).