Partition GHZ SLOCC class of three qubits into ten families under LU

TL;DR

This paper introduces a new classification of three-qubit GHZ SLOCC class states into ten LU families, providing a LU invariant, entanglement measures, and conditions for the generalized Schmidt decomposition's uniqueness.

Contribution

It presents a novel LU-based classification of GHZ SLOCC class states into ten families, enhancing understanding of three-qubit entanglement structure.

Findings

Partitioned GHZ SLOCC class into ten LU families

Developed LU invariant and entanglement measures

Established conditions for generalized Schmidt decomposition uniqueness

Abstract

In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et al. obtained a finite yet systematic classification of multi-particle entanglement. It is well known that under SLOCC, pure states of three (four) qubits are partitioned into six (nine) families. In this paper,we present a LU invariant and an entanglement measures for the GHZ SLOCC class of three qubits, and partition states of the GHZ SLOCC class of three qubits into ten families and each family into two subfamilies under LU. We give a necessary and sufficient condition for the uniqueness of the generalized Schmidt decomposition for the GHZ SLOCC class.