  We show that for a finite-dimensional Hilbert space, there exist observables
that induce a tensor product structure such that the entanglement properties of
any pure state can be tailored. In particular, we provide an explicit, finite
method for constructing observables in an unstructured d-dimensional system so
that an arbitrary known pure state has any Schmidt decomposition with respect
to an induced bipartite tensor product structure. In effect, this article
demonstrates that in a finite-dimensional Hilbert space, entanglement
properties can always be shifted from the state to the observables and all pure
states are equivalent as entanglement resources in the ideal case of complete
control of observables.
