# Entanglement wedge nesting Entanglement wedge nesting is the statement that, if a boundary region whose domain of dependence is contained in that of another region, then the corresponding entanglement wedge of the former region is contained in that of the latter region. Classically, this is ensured by [[0480 Null energy condition|NEC]]. ## Refs - [[2016#Akers, Koeller, Leichenauer, Levine]] - relation to many other conditions - [[2017#Akers, Chandrasekaran, Leichenauer, Levine, Shahbazi-Moghaddam]] - [[2023#Czech, Shuai, Wang, Zhang]]: relation to [[0259 Holographic entropy cone|holographic entropy cones]] ## Relation to the racing condition - see [[2020#Berenstein, Grabovsky]] for the racing condition - EWN => entanglement surfaces are spacelike related if a boundary region belongs to the domain of dependence of another - if tortoise is too slow to go from $A$ to $B$ when the bulk hare is causal, the two boundary regions are totally spacelike -> then $\bar{B}$ contains $A$ -> EWN would make sure that entanglement surfaces are spacelike -> contradiction