Weakly coupled local particle detectors cannot harvest entanglement

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.

36 pages v2: revised version, references added

References in corpus (5)

• Wavepacket detection with the Unruh-DeWitt model
• Relativistic causality in particle detector models: Faster-than-light signalling and "Impossible measurements"
• On the Reeh-Schlieder Property in Curved Spacetime
• Thermal equilibrium states of a linear scalar quantum field in stationary spacetimes
• Separation theorems and Bell inequalities in algebraic quantum mechanics

Cited by in corpus (16)

• A detector-based measurement theory for quantum field theory
• Fully Relativistic Entanglement Harvesting
• Particle Detectors from Localized Quantum Field Theories
• Causal State Updates in Real Scalar Quantum Field Theory
• Entanglement structure of quantum fields through local probes
• How measuring a quantum field affects entanglement harvesting
• Asymptotic measurement schemes for every observable of a quantum field theory
• Transmission of quantum information through quantum fields in curved spacetimes
• Particle detector models from path integrals of localized quantum fields
• The Unruh-DeWitt model and its joint interacting Hilbert space
• Harvesting Fermionic Field Entanglement in Schwarzschild Spacetime
• Detector-based measurements for QFT: two issues and an AQFT proposal
• Localizing quantum fields with time-dependent potentials
• Quantum Field Theory in Successive Rindler Spacetimes
• Quantum kicks near a Cauchy horizon
• Bipartite and tripartite entanglement in pure dephasing relativistic spin-boson model