  Defining quantum information quantities directly in bulk quantum gravity is a
difficult problem due to the fluctuations of spacetime. Some progress was made
recently in \cite{Mertens:2022ujr}, which provided a bulk interpretation of the
Bekenstein Hawking formula for two sided BTZ black holes in terms of the
entanglement entropy of gravitational edge modes. We generalize those results
to give a bulk entanglement entropy interpretation of the quantum extremal
surface formula in AdS3 gravity, as applied to a single interval in the
boundary theory. Our computation further supports the proposal that AdS3
gravity can be viewed as a topological phase in which the bulk gravity edge
modes are anyons transforming under the quantum group
$\SL^{+}_{q}(2,\mathbb{R})$. These edge modes appear when we cut open the
Euclidean path integral along bulk co-dimension 2 slices, and satisfies a
shrinkable boundary condition which ensures that the Gibbons-Hawking
calculation gives the correct state counting.
