  Working with a rather general notion of independence, we provide a
transference method which allows to compare the p-norm of sums of independent
copies with the p-norm of sums of free copies. Our main technique is to
construct explicit operator space Lp embeddings preserving independence to
reduce the problem to L1, where some recent results by the first-named author
can be used. We find applications for noncommutative Khincthine/Rosenthal type
inequalities and for noncommutative Lp embedding theory.
