Dealing with indistinguishable particles and their entanglement

TL;DR

This paper introduces a label-free, particle-based approach to analyze quantum systems of identical particles, effectively addressing issues in quantum correlations and entanglement characterization.

Contribution

It presents a novel multiparticle probability amplitude framework derived from first principles, connecting to second quantization and generalizing entangled states for identical particles.

Findings

The approach avoids methodological problems of standard methods.

Spatial overlap influences entanglement and nonlocal correlations.

Defined spin-exchanged multipartite states (SPES) generalize W states for identical particles.

Abstract

Here we discuss a particle-based approach to deal with systems of many identical quantum objects (particles) which never employs labels to mark them. We show that it avoids both methodological problems and drawbacks in the study of quantum correlations associated to the standard quantum mechanical treatment of identical particles. The core of this approach is represented by the multiparticle probability amplitude whose structure in terms of single-particle amplitudes we here derive by first principles. To characterise entanglement among the identical particles, this new method utilises the same notions, such as partial trace, adopted for nonidentical ones. We highlight the connection between our approach and second quantization. We also define spin-exchanged multipartite states (SPES) which contain a generalisation of W states to identical particles. We prove that their spatial overlap plays a role on the distributed entanglement within multipartite systems and is responsible for the appearance of nonlocal quantum correlations.