How is quantum information localized in gravity?

TL;DR

This paper analyzes how quantum information can be localized in gravity, confronting the challenge that diffeomorphism invariance and gravitational dressings prevent a straightforward LQFT-like subsystem factorization. It compares tensor-factorization, commuting-subalgebras, and split-structure approaches, using QED as a tractable template to illustrate a physically meaningful split structure and its relation to soft hair. Classical gravity is shown to admit localized information through dressings whose exterior fields depend only on the Poincaré charges, while quantum gravity may realize split structures perturbatively—potentially aided by global symmetries—but nonperturbative dynamics (e.g., ADM translations) could obscure locality and threaten such splits. The work emphasizes that soft hair does not generically encode interior information and highlights the delicate interplay between locality, gauge constraints, and nonperturbative gravity in seeking a holographic-like description. Overall, it provides a framework to think about localized information in gravity, clarifies the limits of soft-hair arguments, and identifies key open questions about nonperturbative locality and information transfer.

Abstract

A notion of localization of information within quantum subsystems plays a key role in describing the physics of quantum systems, and in particular is a prerequisite for discussing important concepts such as entanglement and information transfer. While subsystems can be readily defined for finite quantum systems and in local quantum field theory, a corresponding definition for gravitational systems is significantly complicated by the apparent nonlocality arising due to gauge invariance, enforced by the constraints. A related question is whether "soft hair" encodes otherwise localized information, and the question of such localization also remains an important puzzle for proposals that gravity emerges from another structure such as a boundary field theory as in AdS/CFT. This paper describes different approaches to defining local subsystem structure, and shows that at least classically, perturbative gravity has localized subsystems based on a split structure, generalizing the split property of quantum field theory. This, and related arguments for QED, give simple explanations that in these theories there is localized information that is independent of fields outside a region, in particular so that there is no role for "soft hair" in encoding such information. Additional subtleties appear in quantum gravity. We argue that localized information exists in perturbative quantum gravity in the presence of global symmetries, but that nonperturbative dynamics is likely tied to a modification of such structure.