Classification of Bipartite and Tripartite Qutrit Entanglement under SLOCC

TL;DR

This paper classifies bipartite and tripartite qutrit entangled states under SLOCC by analyzing their coefficient matrices, resulting in explicit classifications into distinct equivalence classes.

Contribution

It provides a detailed classification of biqutrit and triqutrit pure states under SLOCC, identifying all equivalence classes explicitly.

Findings

Two classes of biqutrit states identified

Twelve classes of triqutrit states identified

Explicit classification based on singular vector spaces

Abstract

We classify biqutrit and triqutrit pure states under stochastic local operations and classical communication. By investigating the right singular vector spaces of the coefficient matrices of the states, we obtain explicitly two equivalent classes of biqutrit states and twelve equivalent classes of triqutrit states respectively.