<![CDATA[Entanglement classification is a core aspect of quantum information theory. It ensures successful quantum information processing. This article presents a comparative study of entanglement classification using developed operator models for the special unitary group and special linear group. This study was built upon prior work in entanglement classification in a pure three-qubit quantum system environment, where the operator models for each mathematical group were independently developed. Through extensive analysis, both synthesized models are functionally effective and yield the desired results. However, the comparative analysis reveals that the operator model exhibits certain limitations, particularly in its early phase of development compared to. This study provides significant enlightenments into the practical abilities of the developed operator models in entanglement classification and underlines the theoretical distinction between and paving the path for future research in quantum information theory, specifically entanglement classification.]]>
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