Quantum field theory in curved spaces and quantum information theory have joined forces
for several years with the aim of addressing fundamental questions such as: how do quantum theory
and gravity work together? With this in mind, this work presents a local construction of the S-matrix
from a generalization of the LSZ reduction theorem for curved spaces, using local Riemann
coordinates. We performed calculations of elastic scattering at the tree level to analyze corrections
arising from a general curved manifold in quantum correlations. More specifically, we computed the
entanglement entropy generated from scattering between two particles in a scalar field theory phi^3
on a general curved manifold. Our results coincide with some previous literature that analyzed
entanglement entropy in the vicinity of black holes and non-commutative spacetimes