Entanglement wedge reconstruction

Prove that all physical quantities in the entanglement wedge W[B] of a boundary spatial subregion B are represented by operators in the corresponding subregion of the boundary conformal field theory, thereby establishing entanglement wedge reconstruction in general settings.

Background

Bulk reconstruction is essential for demonstrating how local semiclassical bulk observables are encoded in the boundary CFT. The entanglement wedge reconstruction conjecture posits that bulk data in the wedge associated with a boundary region can be represented by boundary operators.

The authors present EWR as the key conjectural tool linking bulk locality to boundary operator algebras, often realized via quantum error-correcting codes that identify a code subspace of the CFT corresponding to semiclassical bulk degrees of freedom.

References

We can now introduce the crucial tool for bulk reconstruction, which is the entanglement wedge reconstruction conjecture, which says that: (EWR) Entanglement wedge reconstruction: all physical quantities in $W[B]$, i.e.\ the entanglement wedge of a spatial subregion $B$, are represented in the CFT by operators in $B$.

— Dualities in Physics  (2509.15866 - Haro et al., 19 Sep 2025) in Section 4.4 AdS-CFT and Bulk Reconstruction (EWR)

There are many open questions for future work. To obtain further information on the smoothness of the horizon and address problems such as the firewall paradox, we need to study the interior dynamics. Our bulk reconstruction algorithm only reconstructs the causal wedge of the boundary, which does not directly determine the interior dynamics. A new principle is needed to determine the interior dynamics from boundary data.

— Blast freezing a black hole  (2609.28962 - Akhtar et al., 24 Sep 2026) in Section “Interior dynamics and future directions”