Gravitational splitting at first order: Quantum information localization in gravity

Abstract: We explore the important fundamental question of how quantum information is localized in quantum gravity, in a perturbative approach. Familiar descriptions of localization of information, such as via tensor factorization of the Hilbert space or a net of commuting subalgebras of operators, conflict with basic gravitational properties -- specifically gauge invariance -- already at leading order in perturbation theory. However, previous work found that information can be classically localized in a region in a way such that measurements, including those of the gravitational field, outside the region are insensitive to that information, and only measure total Poincare charges. This paper shows that, working to leading order in the gravitational coupling, a similar quantum result holds, leading to a definition of a "gravitational splitting" on the Hilbert space for gravity. Such localization of information also argues against a role for "soft hair" in resolving the information problem for black holes. This basic mathematical structure plausibly plays a foundational role in the quantum description of gravity.