Classification of real and complex 3-qutrit states

TL;DR

This paper classifies the orbits of the group SL(3,F)^3 on the tensor space F^3⊗F^3⊗F^3 for real and complex fields, providing insights into the structure of 3-qutrit states and their relevance in physical theories.

Contribution

It offers a complete classification of real and complex 3-qutrit states by analyzing the orbits of SL(3,F)^3 on the tensor space, connecting mathematical structures with physical applications.

Findings

Classification of orbits for F=R and F=C

Overview of physical theories related to 3-qutrit states

Identification of orbit representatives and invariants

Abstract

In this paper we classify the orbits of the group SL(3,F)^3 on the space F^3\otimes F^3\otimes F^3 for F=C and F=R. This is known as the classification of complex and real 3-qutrit states. We also give an overview of physical theories where these classifications are relevant.