  Local state transformation is the problem of transforming an arbitrary number
of copies of a bipartite resource state to a bipartite target state under local
operations. That is, given two bipartite states, is it possible to transform an
arbitrary number of copies of one of them to one copy of the other state under
local operations only? This problem is a hard one in general since we assume
that the number of copies of the resource state is arbitrarily large. In this
paper we prove some bounds on this problem using the hypercontractivity
properties of some super-operators corresponding to bipartite states. We
measure hypercontractivity in terms of both the usual super-operator norms as
well as completely bounded norms.
