Information geometry of quantum entangled Gaussian wave-packets

We apply information geometric (IG) techniques to study s-wave, scattering-induced quantum entanglement. Application of IG methods enables use of statistical manifolds associated with correlated and non-correlated Gaussian probability distribution functions to model the quantum entanglement of two spinless, structureless, non-relativistic particles, the latter represented by minimum uncertainty Gaussian wave-packets. Our analysis leads to the following relevant findings: first, we are able to express the entanglement strength, quantified by the subsystem purity, in terms of scattering potential and incident particle energies, which in turn, are related to the micro-correlation coefficient r, a quantity that parameterizes the correlated microscopic degrees of freedom of the system; second, we show that the entanglement duration can be controlled by the initial momentum, momentum spread and r. Finally, we uncover a quantitative relation between quantum entanglement and information geometric complexity.