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arXiv:2208.13801 · Physical review. D/Physical review. D.

Entanglement harvesting: State dependence and covariance

Héctor Maeso-García, José Polo-Gómez, Eduardo Martín-Martínez

Published Nov 3, 2022• 7 citations
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Abstract

We analyze entanglement harvesting for arbitrary initial states of particle detectors and arbitrary quasifree states of the field. Despite the fact that spatially smeared particle detectors are known to break covariance for arbitrary initial states, we show that the entanglement harvested by a pair of detectors from a quasifree state of a scalar field is a covariant quantity up to second order in perturbation theory.

DOI
10.1103/physrevd.106.105001

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We analyze entanglement harvesting for arbitrary initial states of particle detectors and arbitrary quasifree states of the field. Despite the fact that spatially smeared particle detectors are known to break covariance for arbitrary initial states, we show that the entanglement harvested by a pair of detectors from a quasifree state of a scalar field is a covariant quantity up to second order in perturbation theory.
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We analyzed how entanglement harvesting is affected by the performance of a measurement on the quantum field. The measurement on the field is modeled as the coupling of a particle detector to the field, followed by a projective measurement performed on the detector. In our analysis, we considered different arrangements for two detectors harvesting entanglement and an ancillary detector used to perform a measurement. We found different regimes for how performing measurements on the field affects the entanglement harvested, depending on the initial and final states of the detector used to measure the field, as well as its coupling strength. We identified the regimes where it is possible to measure the field during the preparation of entanglement harvesting protocols without significantly interfering in the entanglement harvested. We also identify in what regimes the field measurement can degrade or slightly enhance the ability of particle detectors to harvest entanglement.
We analyze correlations between pairs of particle detectors quadratically coupled to a real scalar field. We find that, while a single quadratically coupled detector presents no divergences, when one considers pairs of detectors, there emerge unanticipated persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire from the field. We have characterized such divergences, discussed whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally found a UV-safe quantifier of harvested correlations. Our results are relevant to future studies of the entanglement structure of the fermionic vacuum.
We analyze correlations between pairs of detectors quadratically coupled to real and complex scalar bosonic fields in 3+1 dimensions. This is a first step toward studying the entanglement structure of the fermionic vacuum through the entanglement harvesting protocol. We find that, while a single quadratically coupled Unruh-DeWitt presents no divergences, when one considers pairs of detectors there emerge persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire \nfrom the field. These divergences were not anticipated in previous studies. We characterize the divergences, discuss whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally find a UV-safe quantifier of harvested correlations.
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.
We study the protocol of entanglement harvesting when the particle detectors that harvest entanglement from the field are replaced by fully relativistic quantum field theories. We show that two localized modes of the quantum field theories are able to harvest the same amount of leading order entanglement as two nonrelativistic particle detectors, thus implying that quantum field theoretical probes can generally harvest more entanglement than particle detectors. These results legitimize the use of particle detectors to study entanglement harvesting regardless of their internally nonrelativistic nature.