Entanglement of Pure States

But we do not measure wholeness of essence by wholeness of place, and what is wholly in something according to its whole essence can therefore yet be in some manner outside it.

Thomas Aquinas

This will be called the ‘transfer problem’, namely to replace mutual characteristics contained in the relation between bodies by formally similar self characteristics regarded as intrinsic in the bodies.

Arthur Eddington

Bohr maintains that state descriptions of quantum-mechanical systems are relations between the systems and measuring devices in action, and are therefore dependent upon the existence of other systems suitable for carrying out the measurements.

Paul Feyerabend

Abstract

We consider the concept of entanglement for pure cases of finite dimensional state spaces. The criterion of unentangled states is related to demanding rank one of an associated eigenvalue problem. In addition to the conventional procedure based on the Schmidt decomposition, we devise a method based on the spectral resolution of unsymmetric matrices. In particular, we consider the case when all eigenvalues are zero, and find that the method still works.