  We propose that holographic entanglement entropy can be calculated at
arbitrary orders in the bulk Planck constant using the concept of a "quantum
extremal surface": a surface which extremizes the generalized entropy, i.e. the
sum of area and bulk entanglement entropy. At leading order in bulk quantum
corrections, our proposal agrees with the formula of Faulkner, Lewkowycz, and
Maldacena, which was derived only at this order; beyond leading order
corrections, the two conjectures diverge. Quantum extremal surfaces lie outside
the causal domain of influence of the boundary region as well as its
complement, and in some spacetimes there are barriers preventing them from
entering certain regions. We comment on the implications for bulk
reconstruction.
