Leading order corrections to the quantum extremal surface prescription

TL;DR

This paper identifies and corrects leading order errors in the quantum extremal surface (QES) prescription, especially in cases with multiple QES and significant bulk entropy, refining the understanding of entanglement wedge reconstruction.

Contribution

It provides a corrected derivation of the QES prescription accounting for leading order effects and introduces refined conditions for its validity using one-shot quantum Shannon theory.

Findings

Corrected QES prescription for complex bulk entropy scenarios

Refined conditions for QES validity using smooth min- and max-entropies

Reinterpretation of entanglement wedge reconstruction as quantum state merging

Abstract

We show that a na\"{i}ve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently.