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