  In this paper, we study the entanglement entropy between two SYK systems with
bilinear coupling. We use the replica trick to calculate the entanglement
entropy in the ground state. In parallel, we calculate the entanglement entropy
through the Ryu-Takayanagi formula in gravity. For the ground state that is
dual to an eternal traversable wormhole in AdS_2, the bulk quantum correction
to the entanglement entropy is of the same order as the minimal surface area.
The ground state of the coupled system is close to a thermofield double state
with particular temperature and they have the same entanglement entropy. From
the gravity point of view, we explain why the two states have the same
entanglement entropy. We also study a case with time-dependent coupling, which
involves finding the quantum extremal surface in the bulk.
