Remarks on entanglement and identical particles

TL;DR

This paper discusses how entanglement and separability for identical particles depend on the choice of observables and states, proposing a perspective based on the factorization of mean values and comparing it with a recent entropy-based approach.

Contribution

It introduces a natural criterion for separability in identical particles based on observable factorization and compares it with a novel entanglement entropy approach that does not rely on labeling particles.

Findings

Separability depends on the choice of observables and states.

A new entanglement entropy can be defined without labeling particles.

Different approaches to entanglement yield contrasting insights.

Abstract

We argue that in the case of identical particles the most natural identification of separability, that is of absence of non-classical correlations, is via the factorization of mean values of commuting observables. It thus follows that separability and entanglement depend both on the state and on the choice of observables and are not absolute notions. We compare this point of view with a recent novel approach to the entanglement of identical particles, which allows for the definition of an entanglement entropy from a suitably defined reduced particle density matrix, without the need of labeling the system constituents. We contrast this figure of merit with the aforementioned lack of an absolute notion of entanglement by considering few paradigmatic examples.