Quantum null energy condition, entanglement wedge nesting, and quantum focusing

We study the consequences of entanglement wedge nesting for conformal field theories (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 <= 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.