Extremality as a Consistency Condition on Subregion Duality

Understand

In JT gravity coupled to a CFT, I argue without using the path integral that the entanglement wedge of a boundary region is bounded by a quantum extremal surface (QES).

• For any candidate not bounded by a QES, a unitary in the complement can make reconstruction within the candidate inconsistent with boundary causality.
• The case without islands is a direct consequence of subregion duality, and the case with islands can also be dealt with with a stronger assumption.