# Weakly coupled local particle detectors cannot harvest entanglement

March 24, 2021

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.

Keywords:

entanglement harvesting, QFT on curved spacetimes