Validity of decoupling for entanglement structure under in-in time evolution

Determine whether the decoupling theorem holds when analyzing the entanglement structure and entropy-related observables of quantum field theories in flat and curved spacetimes, particularly in settings that study explicit in-in (Schwinger–Keldysh) time evolution of states and observables.

Background

Throughout the paper, the authors reconcile apparent purity loss at order 1/M from tracing out heavy fields with effective field theory expectations by highlighting the role of resolution scales and the iε prescription. While decoupling ensures heavy physics influences low-energy dynamics through local Hamiltonians, which preserve purity, explicit in-in calculations of entanglement measures can show basis-dependent purity changes, raising questions about how decoupling applies to such information-theoretic observables.

The authors note that decoupling is well established for S-matrix (in–out) formulations but emphasize that its validity for entanglement structures and time-evolving observables in in–in frameworks, including curved spacetimes, is not yet settled. Clarifying this would help align effective field theory methods with quantum information measures used in cosmology and other time-dependent settings.