Critical points of the linear entropy for pure L-qubit states

TL;DR

This paper introduces an improved numerical method for identifying critical points of linear entropy in pure L-qubit states, leveraging group theory and momentum maps for enhanced efficiency.

Contribution

It presents a novel approach based on the correspondence between abelian and non-abelian momentum maps, simplifying the computation process.

Findings

Method is more efficient and easier to implement numerically.

Successfully applied to analyze critical points in L-qubit systems.

Enhances understanding of entanglement properties in quantum states.

Abstract

We present a substancially improved version of the method proposed in Sawicki et al (2012, 2014) for finding critical points of the linear entropy for L-qubit system. The new approach is based on the corespondance between momentum maps for abelian and non-abelian groups, as described in Kirwan (1984). The proposed method can be implemented numerically much easier than the previous one.