Proof of a Quantum Bousso Bound

TL;DR

This paper proves the generalized Covariant Entropy Bound for light-sheets in quantum field theory, demonstrating the bound's validity without assuming the null energy condition and considering small gravitational backreaction.

Contribution

It provides a rigorous proof of the quantum Bousso bound for free fields, extending the classical entropy bound to quantum regimes without energy condition assumptions.

Findings

The bound holds for free fields with small backreaction.

Null generators' non-expansion protects the bound where energy conditions fail.

The proof does not rely on the null energy condition.

Abstract

We prove the generalized Covariant Entropy Bound, $\Delta S\leq (A-A')/4G\hbar$, for light-sheets with initial area $A$ and final area $A'$. The entropy $\Delta S$ is defined as a difference of von Neumann entropies of an arbitrary state and the vacuum, with both states restricted to the light-sheet under consideration. The proof applies to free fields, in the limit where gravitational backreaction is small. We do not assume the null energy condition. In regions where it is violated, we find that the bound is protected by the defining property of light-sheets: that their null generators are nowhere expanding.