Locality and entanglement of indistinguishable particles

Till Jonas Frederick Johann,Ugo Marzolino

doi:10.1038/s41598-021-94991-y

Till Jonas Frederick Johann, Ugo Marzolino

Open Access

https://doi.org/10.1038/s41598-021-94991-y

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Journal: Scientific Reports	Publication Date: Jul 29, 2021
Citations: 5	License type: open-access

Affiliation: INFN Sezione di Trieste, Heidelberg University

Abstract

Entanglement is one of the strongest quantum correlation, and is a key ingredient in fundamental aspects of quantum mechanics and a resource for quantum technologies. While entanglement theory is well settled for distinguishable particles, there are five inequivalent approaches to entanglement of indistinguishable particles. We analyse the different definitions of indistinguishable particle entanglement in the light of the locality notion. This notion is specified by two steps: (i) the identification of subsystems by means of their local operators; (ii) the requirement that entanglement represent correlations between the above subsets of operators. We prove that three of the aforementioned five entanglement definitions are incompatible with any locality notion defined as above.

Highlights

Entanglement is one of the strongest quantum correlation, and is a key ingredient in fundamental aspects of quantum mechanics and a resource for quantum technologies
Entanglement theory is very well understood for distinguishable particles: two-particle separable, namely non-entangled, pure states are of the form |ψ1 ⊗ |ψ2, and each subsystem is implicitly assumed to be a particle
We focus on the aforementioned entanglement definitions that do not correspond to particle correlations, and investigate if they rather represent correlations between subsystems identified by general subsets A and B

Summary

Introduction

Entanglement is one of the strongest quantum correlation, and is a key ingredient in fundamental aspects of quantum mechanics and a resource for quantum technologies. Entanglement theory is very well understood for distinguishable particles: two-particle separable, namely non-entangled, pure states are of the form |ψ1 ⊗ |ψ2 , and each subsystem is implicitly assumed to be a particle This definition can be reformulated by describing each subsystem with operators, termed local and acting non-trivially only on it, i.e. A = O1 ⊗ 12 for the first particle and B = 11 ⊗ O2 for the second one. The aforementioned single-particle operators are no longer allowed These considerations challenge the notion of particle as a natural subsystem, whenever indistinguishability cannot be neglected, e.g. if particles are not spatially separated (see Fig. 1 for an illustration of particles that are progressively less separated and lose their distinguishability)

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