Entanglement Equivalence of $N$-qubit Symmetric States

TL;DR

This paper investigates the interconversion of symmetric N-qubit states under SLOCC, establishing that symmetric states can be connected by symmetric ILOs and classifying their entanglement types.

Contribution

It proves that symmetric ILOs suffice for connecting symmetric states under SLOCC and provides a practical method for entanglement class discrimination.

Findings

Symmetric ILOs are sufficient for SLOCC equivalence of symmetric states.

Connected states belong to separable, W, or GHZ classes.

Simplifies experimental implementation of state interconversion.

Abstract

We study the interconversion of multipartite symmetric $N$-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local operation (ILO), then they belong necessarily to the separable, W, or GHZ entanglement class, establishing a practical method of discriminating subsets of entanglement classes. Furthermore, we prove that there always exists a symmetric ILO connecting any pair of symmetric $N$-qubit states equivalent under SLOCC, simplifying the requirements for experimental implementations of local interconversion of those states.