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

TL;DR

This paper demonstrates that in finite-dimensional quantum systems, one can construct observables to induce a tensor product structure, allowing any pure state's entanglement properties to be tailored or shifted to the measurement framework.

Contribution

It provides an explicit finite method to construct observables that can assign any desired entanglement structure to pure states in finite-dimensional systems.

Findings

Existence of observables that induce specific tensor product structures.

Any pure state's entanglement can be tailored via observable design.

All pure states can be considered equivalent as entanglement resources with complete observable control.

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.