  The Bousso bound requires that one quarter the area of a closed codimension
two spacelike surface exceeds the entropy flux across a certain lightsheet
terminating on the surface. The bound can be violated by quantum effects such
as Hawking radiation. It is proposed that at the quantum level the bound be
modified by adding to the area the quantum entanglement entropy across the
surface. The validity of this quantum Bousso bound is proven in a
two-dimensional large N dilaton gravity theory.
