Entanglement Classification via Single Entanglement Measure

TL;DR

This paper demonstrates that a single polynomial entanglement measure can determine SLOCC equivalence of n-qubit states, using geometric interpretations and root-based classification, simplifying entanglement analysis.

Contribution

It introduces a method to classify n-qubit entanglement with one measure and provides a new approach to normalize 4-qubit states efficiently.

Findings

Single polynomial measure suffices for SLOCC classification

Roots of the 3-tangle classify 4-qubit states

Proposed method simplifies 4-qubit state normalization

Abstract

We show that a single polynomial entanglement measure is enough to verify equivalence between generic $n$-qubit states under Stochastic Local Operations with Classical Communication (SLOCC). SLOCC operations may be represented geometrically by M\"obius transformations on the roots of the entanglement measure on the Bloch sphere. Moreover, we show how the roots of the 3-tangle measure classify 4-qubit generic states, and propose a method to obtain the normal form of a 4-qubit state which bypasses the possibly infinite iterative procedure.