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We show that for a finite-dimensional Hilbert space, there exist observablesthat induce a tensor product structure such that the entanglement properties ofany pure state can be tailored. In particular, we provide an explicit, finitemethod for constructing observables in an unstructured d-dimensional system sothat an arbitrary known pure state has any Schmidt decomposition with respectto an induced bipartite tensor product structure. In effect, this articledemonstrates that in a finite-dimensional Hilbert space, entanglementproperties can always be shifted from the state to the observables and all purestates are equivalent as entanglement resources in the ideal case of completecontrol of observables.

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