According to a recent idea, curved bulk space-time is an emergent entity coming from entanglement patterns residing on its boundary. Recently, apart from the bulk and its boundary a new space called kinematic space has been introduced. Kinematic space, which is just the space of geodesics of the bulk, acts as an intermediary that translates between the boundary language of quantum information and entanglement, and the bulk language of gravity and geometry.

Within the framework of the $ADS_3/CFT_2$ duality we show how scattering data of a simple geometric bulk scattering problem can be related to boundary entanglement of the CFT vacuum. This connection enables a calculation of the Berry curvature living on kinematic space. The associated gauge degree of freedom (Berry's Phase) is related to the freedom of regularizing the length spectra of the geodesics of the bulk, or equivalently introducing different cut-offs for the boundary CFT. The Berry curvature turns out to be just the so called Crofton form of kinematic space with a coefficient depending on the scattering energy. We show how the Berry-Crofton form defines a causal structure on kinematic space corresponding to the strong subadditivity structure of entanglement entropy for boundary subsystems. We conjecture that applying results from Algebraic Scattering Theory our ideas can be generalized for more general states corresponding to more general bulk geometries and also the general $AdS_{n+1}/CFT_n$ correspondence.