The paper presents a systematic perturbative expansion for computing the purity and entanglement entropy of quantum fields in curved spacetimes, generalizing the in-in formalism to non-unitary dynamics and non-observable quantum information measures. The authors derive Feynman rules for standard correlation functions and apply their formalism to a cosmological setting inspired by the effective field theory of inflation. They find that at late times, non-linear loop corrections share the same time behavior as linear contributions, only slightly affecting the purity. Specifically, when the environment is heavy compared to the Hubble scale, the phenomenon of recoherence observed previously remains robust. This work bridges the gap between perturbative quantum field theory and open quantum systems, enhancing our understanding of renormalization and resummation in open effective field theories and facilitating a more systematic exploration of quantum information properties in field-theoretic settings.The paper presents a systematic perturbative expansion for computing the purity and entanglement entropy of quantum fields in curved spacetimes, generalizing the in-in formalism to non-unitary dynamics and non-observable quantum information measures. The authors derive Feynman rules for standard correlation functions and apply their formalism to a cosmological setting inspired by the effective field theory of inflation. They find that at late times, non-linear loop corrections share the same time behavior as linear contributions, only slightly affecting the purity. Specifically, when the environment is heavy compared to the Hubble scale, the phenomenon of recoherence observed previously remains robust. This work bridges the gap between perturbative quantum field theory and open quantum systems, enhancing our understanding of renormalization and resummation in open effective field theories and facilitating a more systematic exploration of quantum information properties in field-theoretic settings.