Systematic generation of entanglement measures for pure states

TL;DR

This paper introduces a systematic method to generate and evaluate entanglement measures for pure states in multipartite systems using irreducible decompositions under local unitary transformations, unifying existing measures and creating new ones.

Contribution

The authors develop a general algebraic and experimentally feasible approach to derive entanglement monotones from irreducible representations, applicable to multipartite systems and capable of classifying entanglement.

Findings

Reproduces many known entanglement measures in a unified framework

Provides a method to evaluate measures efficiently through local projective measurements

Introduces new entanglement measures based on non-singlet representations

Abstract

We propose a method to generate entanglement measures systematically by using the irreducible decomposition of some copies of a state under the local unitary (LU) transformations. It is applicable to general multipartite systems. We show that there are entanglement monotones corresponding to singlet representations of the LU group. They can be evaluated efficiently in an algebraic way, and experimentally measurable by local projective measurements of the copies of the state. Non-singlet representations are also shown to be useful to classify entanglement. Our method reproduces many well-known measures in a unified way, and produces also a lot of new ones.