Unconditional uniqueness for the cubic Gross-Pitaevskii hierarchy via quantum de Finetti

We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in $\R^3$. One of the main tools in our analysis is the quantum de Finetti theorem. Our uniqueness result is equivalent to the one established in the celebrated works of Erd\"os, Schlein and Yau, \cite{esy1,esy2,esy3,esy4}.