Proof of a Quantum Bousso Bound

Understand

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.