Restricted quantum focusing

Quantum focusing is a powerful conjecture that plays a key role in the current proofs of many well-known quantum gravity theorems, including various consistency conditions, and causality constraints in AdS/CFT. We conjecture a (weaker) restricted quantum focusing, which we argue is sufficient to derive all known essential implications of quantum focusing. Subject to a technical assumption, we prove this conjecture in braneworld semiclassical gravity theories that are holographically dual to Einstein gravity in a higher-dimensional anti--de Sitter spacetime.