Entanglement Classification for a Three-qubit System using Special Unitary Groups, SU(2) and SU(4)

Entanglement is a physical phenomenon that links a pair, or a set of particles that correlates with each other, regardless of the distance between them. Recent researches conducted on entanglement are mostly focused on measurement and classification in multiqubit systems. Classification of two qubits will only distinguish the quantum state as either separable or entangled, and it can be done by measurement. Meanwhile, in a three-qubit system, it becomes more complex because of the structure of the three qubits itself. It is not sufficient to do measurement because the states are divided into three types, including fully separable state, biseparable state, and genuine entangled state. Therefore, the classification is needed to distinguish the type of states in the three-qubit system. This study aims to classify the entanglement of three-qubit pure states using a combination model of special unitary groups, SU(2) and SU(4), by changing the angle of selected parameters in SU(4) and acting on the separable pure state. The matrix represents SU(2) is 2×2 matrix while matrix for SU(4) is 4×4 matrix. Hence, the combination of SU(2) and SU(4) represent 8×8 matrix. This classification uses the von Neumann entropy and three tangle measurements to classify the class, respectively. The results of this study have indicated that the three-qubit pure state has been successfully classified into different classes, namely, A-B-C, A-BC, C-AB, GHZ, and W, with A-B-C being a fully separable state, A-BC and C-AB are biseparable states, and GHZ and W are genuine entangled states. The results show that this model can change separable pure states to other entanglement class after transformation is done.

@article{Mohd2019,
  title     = {Entanglement Classification for a Three-qubit System using Special Unitary Groups, SU(2) and SU(4)},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {10},
  number    = {7},
  year      = {2019},
  publisher = {The Science and Information Organization},
  author    = {Siti Munirah Mohd and Bahari Idrus and Hishamuddin Zainuddin and Muriati Mukhtar},
  doi       = {10.14569/IJACSA.2019.0100751},
  url       = {https://doi.org/10.14569/IJACSA.2019.0100751}
}