Operational Families of Entanglement Classes for Symmetric $N$-Qubit States

TL;DR

This paper classifies entanglement types of symmetric N-qubit states under SLOCC, introducing parameters that simplify identifying entanglement families and revealing their growth pattern.

Contribution

It provides a complete classification method for symmetric N-qubit entanglement using diversity and degeneracy parameters, a novel approach in the field.

Findings

Introduces diversity degree and degeneracy configuration as key parameters.

Provides a simple method to identify SLOCC entanglement families.

Shows the number of families grows with the partition function of qubits.

Abstract

We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for all multipartite symmetric states in the general $N$-qubit case. For this purpose, we introduce 2 parameters playing a crucial role, namely the \emph{diversity degree} and the \emph{degeneracy configuration} of a symmetric state. Those parameters give rise to a simple method of identifying operational families of SLOCC entanglement classes of all symmetric $N$-qubit states, where the number of families grows as the partition function of the number of qubits.