Entanglement Classification For Three-qubit Pure Quantum System Using Special Linear Group Under The Slocc Protocol

Quantum technology has been introduced in the IR 4.0, breeding a new era of advanced technology revolutionizing the future. Hence, understanding the key resources of quantum technology, quantum entanglement is vital. Growing interests in quantum technologies has raised comprehensive studies of
quantum entanglement, especially on the entanglement classification. Special Linear group, SL(n) of multipartite entanglement classification under the SLOCC protocol is not widely studied due to its complex structure, creating a curb in developing its classification method. Therefore, this paper developed and delivered a classification method of puremultipartite, three-qubit quantum state using a combination of Special Linear group, SL(2) x SL(2) x SL(2) model operator under the SLOCC, classifying entanglement using the model
operator with certain selected parameters. Further analysis was done resulting in the determination of the six subgroups, namely fully separable (A-B-C), bi-separable (A-BC, B-AC and C-AB) and genuinely entangled (W and GHZ).