On the questions of asymptotic recoverability of information and subsystems in quantum gravity

TL;DR

This paper investigates how quantum information localization and subsystem definitions are affected by gauge constraints in quantum gravity, analyzing the implications for holography and black hole unitarity, with a focus on perturbative versus nonperturbative solutions.

Contribution

It provides a detailed analysis of how gauge constraints influence information recoverability and subsystem definitions in quantum gravity, clarifying the role of perturbative and nonperturbative solutions.

Findings

Perturbative effects on information recovery are exponentially suppressed.

Gauge constraints modify locality properties of operators in quantum gravity.

Implications for black hole unitarity and holography are discussed.

Abstract

A longstanding question in quantum gravity regards the localization of quantum information; one way to formulate this question is to ask how subsystems can be defined in quantum-gravitational systems. The gauge symmetry and necessity of solving the constraints appear to imply that the answers to this question here are different than in finite quantum systems, or in local quantum field theory. Specifically, the constraints can be solved by providing a "gravitational dressing" for the underlying field-theory operators, but this modifies their locality properties. It has been argued that holography itself may be explained through this role of the gauge symmetry and constraints, at the nonperturbative level, but there are also subtleties in constructing a holographic map in this approach. There are also claims that holography is implied even by perturbative solution of the constraints. This short note provides further examination of these questions, and in particular investigates to what extent perturbative or nonperturbative solution of the constraints implies that information naively thought to be localized can be recovered by asymptotic measurements, and the relevance of this in defining subsystems. In the leading perturbative case, the relevant effects are seen to be exponentially suppressed. These questions are, for example, important in sharply characterizing the unitarity problem for black holes.