Entanglement structure of quantum fields through local probes

Abstract

We present a framework to study the entanglement structure of a quantum field theory inspired by the formalism of particle detectors in relativistic quantum information. This framework can in principle be used to faithfully capture entanglement in a QFT between arbitrary-shaped regions of spacetime without encountering UV divergences, bypassing many of the issues typically present in other approaches. Our results also establish the limits of the efficiency of entanglement harvesting, and may also be used to motivate an operational definition of entanglement between spacetime subregions in field theory.

Generalization of Gisin’s theorem to quantum fields

“…In recent years, one observes an increasing interest in the analysis of entanglement of quantum fields in curved spacetimes [48][49][50] in pursuit of finding the nature of gravity, and also in multiple relativistic scenarios [51][52][53] that pose related mathematical problems. One of the main difficulties in such cases is the appearance of inequivalent representations of Fock spaces for different observers, which results in a lack of unambiguous description of particles, making the problem of entanglement much more subtle.…”

“…) for all t are locally orthogonal. Therefore, equation (53) gives Schmidt form for total state with ancillary modes.…”