Bulk Reconstruction Beyond the Entanglement Wedge

TL;DR

This paper investigates the extent of bulk geometry reconstruction in holography, revealing scenarios where the reconstructed region extends beyond the entanglement wedge, challenging traditional views on holographic duality.

Contribution

It demonstrates that the bulk region reconstructible from boundary data can extend beyond the entanglement wedge, questioning established holographic duality principles.

Findings

Bulk reconstruction can reach outside the entanglement wedge.

Minimal surface areas relate to boundary operator expectation values.

Implications for holographic subregion duality and the holographic dictionary.

Abstract

We study the portion of an asymptotically Anti de Sitter geometry's bulk where the metric can be reconstructed, given the areas of minimal 2-surfaces anchored to a fixed boundary subregion. We exhibit situations in which this region can reach parametrically far outside of the entanglement wedge. If the setting is furthermore holographic, so that the bulk geometry is dual to a state in a conformal field theory (CFT), these minimal 2-surface areas can be deduced from the expectation values of operators localized within the boundary subregion. This presents us with an alternative: Either the reduced CFT state encodes significant information about the bulk beyond the entanglement wedge, challenging conventional intuition about holographic subregion duality; or the reduced CFT state fails to contain information about operators whose expectation values give the areas of minimal 2-surfaces anchored within that subregion, challenging conventional intuition about the holographic dictionary.