Leading order corrections to the quantum extremal surface prescription

Understand

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.