A Quantum Bousso Bound

TL;DR

The paper addresses quantum violations of the classical Bousso bound by introducing a quantum correction based on entanglement entropy across the bounding surface. It proposes a quantum Bousso bound using a quantum-corrected area $A_{\text{qu}} = A_{\text{cl}} + 4 S_{\text{ent}}$ and proves it in a two-dimensional, large-N dilaton gravity setting (RST/CGHS with backreaction). The work extends the classical covariant entropy bound to semiclassical gravity, connects to the generalized second law, and clarifies how entanglement entropy and vacuum choices influence bound saturation. This provides a rigorous semiclassical covariant entropy bound compatible with Hawking radiation and highlights the role of quantum information in gravitational entropy bounds.

Abstract

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.