Limits on entanglement from rotationally invariant scattering of spin systems

Abstract

This paper investigates the dynamical generation of entanglement in scattering systems, in particular two spin systems that interact via rotationally invariant scattering. The spin degrees of freedom of the in states are assumed to be in unentangled, pure states, as defined by the entropy of entanglement. Because of the restriction of rotationally symmetric interactions, perfectly entangling $S$ matrices, i.e., those that lead to a maximally entangled out state, only exist for a certain class of separable in states. Using Clebsch-Gordan coefficients for the rotation group, the scattering phases that determine the $S$ matrix are determined for the case of spin systems with $\ensuremath{\sigma}=1∕2$, 1, and $3∕2$.