Bousso–Fisher–Leichenauer–Wall (BFLW) Quantum Bousso Bound

Prove that for any quantum lightsheet L_qu(γ1, γ2) in semiclassical gravity, the fine-grained entropy change S(L_qu(γ1,γ2)) is bounded by the classical area difference, i.e., S(L_qu(γ1,γ2)) ≤ (Area(γ1) − Area(γ2))/(4G), with S(L_qu) defined as the von Neumann entropy difference across slices bounded by γ1 and γ2.

Background

This conjecture follows from the QFC (or rQFC) and reformulates the Bousso bound in terms of fine-grained generalized entropy, avoiding coarse-graining and making the statement cutoff-independent. The thesis connects this bound to rQFC and proves it in JT gravity under appropriate conditions.

References

Conjecture [BFLW quantum Bousso bound] Let $\mathcal{L}{\rm qu}(\gamma_1,\gamma_2)$ be a quantum lightsheet that emanates and terminates orthogonally from two codimension-two spacelike hypersurfaces $\gamma_1$ and $\gamma_2$. Then, \begin{equation} \label{eq:BFLWQBB} S(\mathcal{L}{\rm qu}(\gamma_1,\gamma_2)) \leq \frac{\text{Area}(\gamma_1)-\text{Area}(\gamma_2)}{4G}. \end{equation} We defined \begin{equation} S(\mathcal{L}_{\rm qu}(\gamma_1,\gamma_2)) = S(\Sigma_2) - S(\Sigma_1), \end{equation} where $S(\Sigma_i)$ is the entropy of fields in $\Sigma_i$, a spacelike slice bounded by $\gamma_i$.

— Information-theoretic constraints in quantum gravity and cosmology (2510.15787 - Franken, 17 Oct 2025) in Chapter: Entropy and energy bounds in semiclassical gravity, Section: Quantum Bousso Bounds