Entanglement classification – a comparative study of SU (2) and SL (2) developed operator model

Abstract

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.