A physical protocol for observers near the boundary to obtain bulk information in quantum gravity

TL;DR

This work demonstrates that in a theory of gravity on global AdS, observers confined to a near-boundary region can, in fact, reconstruct the entire low-energy bulk state by exploiting gravitational backreaction and vacuum entanglement. The authors propose a concrete protocol that combines small boundary unitaries, energy measurements, and a basis of states |X⟩ = X|0⟩ to determine overlaps with all bulk energy eigenstates up to a UV cutoff Λ, including handling phases via reference operators and a verification step. They contrast this gravitational result with non-gravitational local quantum field theories, where the split property prevents any interior information from being inferred by boundary observers, and discuss special cases with non-gravitational gauge theories and priors. The findings provide perturbative evidence that holography is encoded in low-energy gravity, with implications for quantum information measures, black hole interiors, and potential obstructions to implementing such protocols in more general settings.

Abstract

We consider a set of observers who live near the boundary of global AdS, and are allowed to act only with simple low-energy unitaries and make measurements in a small interval of time. The observers are not allowed to leave the near-boundary region. We describe a physical protocol that nevertheless allows these observers to obtain detailed information about the bulk state. This protocol utilizes the leading gravitational back-reaction of a bulk excitation on the metric, and also relies on the entanglement-structure of the vacuum. For low-energy states, we show how the near-boundary observers can use this protocol to completely identify the bulk state. We explain why the protocol fails completely in theories without gravity, including non-gravitational gauge theories. This provides perturbative evidence for the claim that one of the signatures of holography -- the fact that information about the bulk is also available near the boundary -- is already visible in the low-energy theory of gravity.

Figures (4)

• Figure 1: On the left, we have the precise setup of this paper. The observers can make manipulations and measurements in a small time band (shaded in red) near the boundary of AdS. This is physically similar to the picture on the right, where the observers can explore an annular region near the boundary of a Cauchy slice that runs through the bulk.
• Figure 2: A flowchart describing the key steps in our protocol.
• Figure 3: In a local QFT, the algebra ${\cal A}_{\text{bulk}}$ supported in the inner region (green) exactly commutes with the algebra ${\cal A}_{[0, \epsilon]}$ supported in the outermost region (red). The "split property" of local QFTs tells us that when the regions are separated by a small "collar" (blue region), the wavefunctions of the two regions can be prepared absolutely independently. The discussion of section \ref{['secprotocol']} tells us that in a theory with dynamical gravity, split states do not exist for the configuration above.
• Figure 4: The figure displays the error $\Delta_{m_{\text{max}}}$ in approximating a state as a function of $m_{\text{max}}$ for two low-energy states. It is evident that this declines monotonically as $m_{\text{max}}$ is increased and becomes very small.