Strengthened convergence of marginals to the cubic nonlinear Schrödinger equation

We rewrite a recent derivation of the cubic non-linear Schrodinger equation by Adami, Golse, and Teta in the more natural form of the asymptotic factorisation of marginals at any fixed time and in the trace norm. This is the standard form in which the emergence of the non-linear effective dynamics of a large system of interacting bosons is proved in the literature