# Entanglement of indistinguishable particles: a comparative study

## TL;DR

This paper compares the Lo Franco and Compagno (LFC) approach with the second quantization formalism for quantifying entanglement in indistinguishable particles, highlighting the role of basis choice and exchange correlations.

## Contribution

It demonstrates how the LFC approach can be derived using second quantization and compares the effects of local versus nonlocal bases on entanglement quantification.

## Key findings

- LFC approach can be recovered via second quantization.
- The basis choice affects the partial trace and entanglement measures.
- Exchange correlations influence entanglement quantification.

## Abstract

There is a debate in course about the quantification of entanglement of indistinguishable particles and recently a new method due to Lo Franco and Compagno (LFC) [Sci. Rep. \textbf{6}, 20603 (2016)] appeared with the aim of settling the controversies of this debate. In this work we show that the LFC approach can be recovered using the second quantization formalism and a local single-particle basis to perform the trace over one particle state. The use of the second quantization formalism has the advantage of being well known in many-body physics. We also compare the LFC and second quantization approaches, or equivalently, the effect of the partial trace over one particle depending on the local and nonlocal caracter of the single-particle basis. Additionally, we study the role played by the exchange correlations in the quantification of entanglement of indistinguishable particles.