  We study holographic entanglement entropy in four-dimensional quantum gravity
with negative cosmological constant. By using the replica trick and evaluating
path integrals in the minisuperspace approximation, in conjunction with the
Wheeler-DeWitt equation, we compute quantum corrections to the holographic
entanglement entropy for a circular entangling surface on the boundary three
sphere. Similarly to our previous work on the sphere partition function, the
path integrals are dominated by a replica version of asymptotically AdS conic
geometries at saddle points. As expected from a general CFT argument, the final
result is minus the free energy on the three sphere which agrees with the
logarithm of the Airy partition function for the ABJM theory that sums up all
perturbative $1/N$ corrections despite the absence of supersymmetries. The
all-order holographic entanglement entropy cleanly splits into two parts, (1)
the $1/N$-corrected Ryu-Takayanagi minimal surface area and (2) the bulk
entanglement entropy across the minimal surface, as suggested in the earlier
literature. It is explicitly shown that the former comes from the localized
conical singularity of the replica geometries and the latter from the
replication of the bulk volume.
