With Chandramouli and Olga: “A physical protocol for observers near the boundary to obtain bulk information in quantum gravity”.
https://arxiv.org/abs/2008.01740
Think of observers who live near the boundary of global AdS and can only explore the spacetime on a single Cauchy slice at large values of the radial coordinate. We put the theory in a low-energy state, and ask these observers to glean as much information they can about the state, without ever directly entering the bulk. How much information can they get?
In a local quantum field theory, the answer is obviously “nothing”. The observers are spatially separated from the region in the middle of AdS, and so operators there commute with all observables accessible to the observers.
It turns out that when gravity is turned on, the surprising answer is “everything”! We develop a protocol, which involves only simple manipulations of the state, and simple measurements from the near-boundary region, and allows the observers to completely determine the state of the bulk.
This is a perturbative check of the idea that signatures of holography are already implicit in semiclassical gravity. It is also closely related to one of the lessons that we learn from a study of black-hole evaporation: information about the interior is also available in a scrambled form in the exterior. This has been discussed for several years — most recently in all the work on “islands” — and so what we have here is a controlled example, where a very similar effect can be studied precisely, and directly in a Lorentzian setting.
Another implication is for quantum information measures. If the von Neumann entropy is understood physically as a measure of lack-of-information, then our result suggests that the von Neumann entropy of an “annular region” (Fig 1b) between r = r0 and r = \infty is zero in a theory of gravity. This is very different from the local QFT result, which would be proportional to r0^(d-1). (Remember, this region is not the entanglement wedge of any subregion on the boundary.)
There has been a lot of recent discussion of the entanglement entropy of regions in theories of gravity, but I think adequate thought isn’t being given to what this quantity means. The idea seems to be do a calculation where gravity switches off exactly at some point, and then just claim that the same result should hold in the presence of dynamical gravity because the corrections must be “small” when gravity is weak. But the fine-grained entropy is not a perturbative quantity, and so the idea that “weak gravity = no gravity” is just wrong in some cases, as this example shows!
If you have questions, comments or, especially, criticism, please email.
Shared link arxiv.org https://www.arxiv.org/abs/2008.01740