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arXiv:1808.01764 · Progress of Theoretical and Experimental Physics

Pure state entanglement harvesting in quantum field theory

Jose Trevison, Koji Yamaguchi, Masahiro Hotta

Published Sep 26, 2018• 17 citations
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Abstract

Quantum fields in vacuum states carry an infinite amount of quantum entanglement, and its entanglement entropy has ultraviolet divergence. Harvesting protocols of the vacuum entanglement have been investigated, but its efficiency is very low to date. The main reason for the low efficiency originates from the fact that the extracted entanglement is embedded in a mixed state of two external devices. We propose a general protocol with high efficiency by extracting pure state entanglement from the field. We only use bi-linear interactions between the fields and external devices. Even though the ultraviolet cutoff remains finite, the protocol is capable of extracting a huge amount of entanglement. Hence an infinite amount of entanglement extraction is attained without the ultraviolet divergence of the field entanglement entropy in a continuum limit. There exists a trade-off relation between the extracted entanglement and its energy cost.

DOI
10.1093/ptep/pty109

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Magic is the quantum resource allowing a quantum computer to perform operations that cannot be simulated efficiently by classical computation. As such, generating magic in a quantum system is crucial for achieving quantum advantage. This article shows that magic can be harvested by a three-level Unruh-DeWitt detector (a qutrit) interacting with a quantum field in an initial vacuum state. While the idea of extracting resources from Quantum Field Theories (QFT) was born from the harvesting of entanglement, our result extends the protocol to evolve a qutrit from a nonmagical state to a magical one, making it possible to generate magic from QFT.
Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined unless an ultraviolet cutoff is introduced, but it still diverges in the continuum limit. This behavior is generic for arbitrary finite-energy states, hence a conceptual tension with the finite entanglement entropy typical of nonrelativistic quantum systems. We introduce a novel approach to explain the transition from infinite to finite entanglement, based on coarse graining the spatial resolution of the detectors measuring the field state. We show that states with a finite number of particles become localized, allowing an identification between a region of space and the nonrelativistic degrees of freedom of the particles therein contained, and that the renormalized entropy of finite-energy states reduces to the entanglement entropy of nonrelativistic quantum mechanics.
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.
We demonstrate the presence of multimode entanglement in the vacuum state of a free, massless scalar quantum field in four-dimensional flat spacetime between two sets of field modes, each contained within a spacetime region that is causally disconnected from the other. This is true despite the fact that entanglement between pairs of individual field modes is sparse and appears only when the two individual modes are carefully selected. Our results reveal that, while entanglement between individual modes is limited, bipartite multimode entanglement in quantum field theory is ubiquitous. We further argue that such multimode entanglement is operationally extractable, and it forms the basis of the entanglement commonly discussed in entanglement harvesting protocols.