Entanglement for all quantum states

TL;DR

This paper demonstrates that entanglement in quantum systems depends on the choice of degrees of freedom, showing that all states can be entangled under some tensor product structure, highlighting its ubiquity.

Contribution

It provides a general proof that entanglement is basis-dependent and can be introduced by changing the degrees of freedom in quantum systems.

Findings

Any factorizable state can become entangled under a different tensor product structure

Entanglement is not an intrinsic property but depends on the choice of degrees of freedom

The paper includes simple examples illustrating the basis dependence of entanglement

Abstract

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.