In-in formalism for the entropy of quantum fields in curved spacetimes

TL;DR

This paper develops a systematic perturbative method using a generalized in-in formalism to compute quantum entanglement entropy in curved spacetimes, with applications to cosmology and insights into open quantum systems.

Contribution

It introduces a novel diagrammatic approach for calculating quantum information measures in non-unitary quantum field theories in curved backgrounds.

Findings

Loop corrections have similar time dependence as linear terms.

Recoherence persists when the environment is heavy.

The formalism links quantum field theory with open quantum systems.

Abstract

We show how to compute the purity and entanglement entropy for quantum fields in a systematic perturbative expansion. To that end, we generalize the in-in formalism to non-unitary dynamics (i.e. accounting for the presence of an environment) and to the calculation of quantum information measures, which are not observables in the usual sense. This allows us to reduce the problem to one involving standard correlation functions, and to organize their computation in a diagrammatic expansion for which we construct the corresponding Feynman rules. As an illustration, we apply the formalism to a cosmological setting inspired by the effective field theory of inflation. We find that at late times, non-linear loop corrections share the same time behavior as the linear contribution, and only yield a slight redressing of the purity. In particular, when the environment is heavy compared to the Hubble scale, the phenomenon of recoherence previously encountered is robust to the class of non-linear extensions considered. Bridging the gap between perturbative quantum field theory and open quantum systems paves the way to a better understanding of renormalization and resummation in open effective field theories. It also enables a more systematic exploration of quantum information properties in field theoretic settings.