Locality and entanglement of indistinguishable particles

TL;DR

This paper examines various definitions of entanglement for indistinguishable particles, analyzing their compatibility with a formal notion of locality, and finds that some definitions are incompatible with this locality concept.

Contribution

It provides a systematic analysis of five entanglement definitions for indistinguishable particles in relation to a formal locality notion, identifying incompatibilities.

Findings

Three entanglement definitions are incompatible with the locality notion.

The locality notion is based on local operators and correlations between their subsets.

The analysis clarifies conceptual foundations of indistinguishable particle entanglement.

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.