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By rearranging its terms, the Quantum Focusing Conjecture (QFC) can be viewedas a quantum energy condition, and we can consider various limits. A recentrestricted version is a limiting form where the quantum focusing vanishes$\Theta \rightarrow 0$, and has been proven for Braneworld scenario. As aresult, we derive an improved quantum null energy condition (INEC) $T_{kk}\geq\frac{\hbar}{2\pi \mathcal{A}}\left(S''_{out}-\frac{1}{2}\thetaS'_{out}\right)$, that can be proven with field theory techniques. We sketchthe beginning of a proof, and briefly discuss possible interpretations in theabsence of one.

The Quantum Focusing Conjecture and the Improved Energy Condition