  We study the consequences of Entanglement Wedge Nesting for CFTs with
holographic duals. The CFT is formulated on an arbitrary curved background, and
we include the effects of curvature-squared couplings in the bulk. In this
setup we find necessary and sufficient conditions for Entanglement Wedge
Nesting to imply the Quantum Null Energy Condition in $d\leq 5$, extending its
earlier holographic proofs. We also show that the Quantum Focusing Conjecture
yields the Quantum Null Energy Condition as its nongravitational limit under
these same conditions.
