Weakly coupled local particle detectors cannot harvest entanglement

TL;DR

The paper demonstrates that local particle detectors cannot harvest entanglement from quantum fields below a certain coupling strength, due to the mixed nature of Reeh-Schlieder states on local modes.

Contribution

It introduces a model-independent, local, and covariant entanglement harvesting protocol using local probes of quantum fields and shows fundamental limitations in entanglement extraction.

Findings

Local particle detectors cannot harvest entanglement below a critical coupling strength.

Reeh-Schlieder states restrict to truly mixed states on local modes.

Entanglement harvesting is limited by the initial state and coupling strength.

Abstract

Many states of linear real scalar quantum fields (in particular Reeh-Schlieder states) on flat as well as curved spacetime are entangled on spacelike separated local algebras of observables. It has been argued that this entanglement can be "harvested" by a pair of so-called particle detectors, for example singularly or non-locally coupled quantum mechanical harmonic oscillator Unruh detectors. In an attempt to avoid such imperfect coupling, we analyse a model-independent local and covariant entanglement harvesting protocol based on the local probes of a recently proposed measurement theory of quantum fields. We then introduce the notion of a local particle detector concretely given by a local mode of a linear real scalar probe field on possibly curved spacetime and possibly under the influence of external fields. In a non-perturbative analysis we find that local particle detectors cannot harvest entanglement below a critical coupling strength when the corresponding probe fields are initially prepared in quasi-free Reeh-Schlieder states and are coupled to a system field prepared in a quasi-free state. This is a consequence of the fact that Reeh-Schlieder states restrict to truly mixed states on any local mode.