  Quantum extremal surfaces are central to the connection between quantum
information theory and quantum gravity and they have played a prominent role in
the recent progress on the information paradox. We initiate a program to
systematically link these surfaces to the microscopic data of the dual
conformal field theory, namely the scaling dimensions of local operators and
their OPE coefficients. We consider CFT states obtained by acting on the vacuum
with single-trace operators, which are dual to one-particle states of the bulk
theory. Focusing on AdS$_3$/CFT$_2$, we compute the CFT entanglement entropy to
second order in the large $c$ expansion where quantum extremality becomes
important and match it to the expectation value of the bulk area operator. We
show that to this order, the Virasoro identity block contributes solely to the
area operator.
