  We introduce variants of relative entropy of entanglement based on the
optimal distinguishability from unentangled states by means of restricted
measurements. In this way, we are able to prove that the standard regularized
entropy of entanglement is strictly positive for all multipartite entangled
states. In particular, this implies that the asymptotic creation of a
multipartite entangled state by means of local operations and classical
communication always requires the consumption of a non-local resource at a
strictly positive rate.
