Rank-based SLOCC classification for odd n qubits

TL;DR

This paper introduces a rank-based method for classifying entanglement in odd n-qubit pure states under SLOCC, dividing the state space into 3^n families based on qubit-specific ranks.

Contribution

It proposes a novel rank-based classification scheme for odd n-qubit states under SLOCC, expanding the understanding of entanglement structures.

Findings

Classification into 3^n families based on qubit ranks

Provides a systematic framework for entanglement classification

Enhances understanding of odd n-qubit entanglement structures

Abstract

We study the entanglement classification under stochastic local operations and classical communication (SLOCC) for odd n-qubit pure states. For this purpose, we introduce the rank with respect to qubit i for an odd n-qubit state. The ranks with respect to qubits 1,2,...,n give rise to the classification of the space of odd n qubits into 3^n families.