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arXiv:2210.05692 · Physical review. D/Physical review. D.

How measuring a quantum field affects entanglement harvesting

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

Published Feb 21, 2023• 15 citations

Abstract

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.

DOI: 10.1103/physrevd.107.045011

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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 explore entanglement harvesting with particle detectors that couple linearly to non-Hermitian fields. Specifically, we analyze the case of particle detectors coupled to a complex scalar quantum field and to a spin

1/2

fermionic field. We find that the complex scalar model can be a good approximation for the fermionic model in the protocol of entanglement harvesting when the mass of the field is sufficiently large compared to the inverse interaction time. Moreover, we show that taking advantage of the

U(1)

degree of freedom of a complex detector it is possible to increase the harvested negativity by up to two orders of magnitude when compared to the case of a real detector.

We explore entanglement harvesting with particle detectors that couple linearly to non-Hermitian fields. Specifically, we analyze the case of particle detectors coupled to a complex scalar quantum field and to a spin 1/2 fermionic field. We then compare these models with the well-known case of a real scalar field and previous results using quadratic models. Unlike quadratic models, the linear models are able to distinguish the particle from the anti-particle sector of the field. This leads to striking differences between quadratic couplings -- which cannot be related to physically observable processes -- and linear couplings -- that can be related to high-energy physics. Finally, we use this analysis to comment on the role that the field statistics plays on the protocol.

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