Observables can be tailored to change the entanglement of any pure state

Abstract

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.