Freudenthal triple classification of three-qubit entanglement

TL;DR

This paper establishes a mathematical classification of three-qubit entanglement types using Freudenthal triple systems, linking quantum states to algebraic structures and computing their SLOCC orbits.

Contribution

It introduces a novel algebraic framework for classifying three-qubit entanglement via Freudenthal triple systems over Jordan algebras.

Findings

Classifies all three-qubit entanglement types with algebraic ranks

Maps entanglement classes to ranks in Freudenthal triple system

Calculates SLOCC orbits for each entanglement class

Abstract

We show that the three-qubit entanglement classes: (0) Null, (1) Separable A-B-C, (2a) Biseparable A-BC, (2b) Biseparable B-CA, (2c) Biseparable C-AB, (3) W and (4) GHZ correspond respectively to ranks 0, 1, 2a, 2b, 2c, 3 and 4 of a Freudenthal triple system defined over the Jordan algebra C+C+C. We also compute the corresponding SLOCC orbits.