  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}.
