Bootstrapping quantum extremal surfaces. Part I. The area operator

A bstract Quantum extremal surfaces are central to the connection between quantum information theory and gravity they have played a prominent role in recent progress on paradox. We initiate program systematically link these microscopic data of dual conformal field theory, namely scaling dimensions local operators their OPE coefficients. consider CFT states obtained by acting vacuum with single-trace operators, which one-particle bulk theory. Focusing AdS 3 /CFT 2 , we compute entanglement entropy second order large c expansion where extremality becomes important match it expectation value area operator. show that this order, Virasoro identity block contributes solely