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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.

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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