The Schmidt number as a universal entanglement measure

TL;DR

This paper introduces the Schmidt number as a universal entanglement measure invariant under local invertible operations, providing a broad quantification of entanglement with applications to specific quantum tasks.

Contribution

It establishes the Schmidt number as a universal entanglement measure and defines pseudo-measures for task-specific entanglement quantification.

Findings

Schmidt number is a universal entanglement measure.

Invariance of entanglement under local invertible operations is proven.

Operational measures include accessible observables in experiments.

Abstract

The class of local invertible operations is defined and the invariance of entanglement under such operations is established. For the quantification of entanglement, universal entanglement measures are defined, which are invariant under local invertible transformations. They quantify entanglement in a very general sense. It is shown that the Schmidt number is a universal entanglement measure, which is most important for the general amount of entanglement. For special applications, pseudo-measures are defined to quantify the useful entanglement for a certain quantum task. The entanglement quantification is further specified by operational measures, which include the accessible observables by a given experimental setup.