  Modular Berry transport is a useful way to understand how geometric bulk
information is encoded in the boundary CFT: The modular curvature is directly
related to the bulk Riemann curvature. We extend this approach by studying
modular transport in the presence of a non-trivial quantum extremal surface.
Focusing on JT gravity on an AdS background coupled to a non-gravitating bath,
we compute the modular curvature of an interval in the bath in the presence of
an island: the Quantum Extremal Modular Curvature (QEMC). We highlight some
important properties of the QEMC, most importantly that it is non-local in
general. In an OPE limit, the QEMC becomes local and probes the bulk Riemann
curvature in regions with an island. Our work gives a new approach to probe
physics behind horizons.
