Abstract
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.
Highlights
The application of entanglement concept is known to be predominant in quantum computers
This is due to the fact that in reality, quantum computers require more than three qubits to access data during high capacity information transmission
An assumption was made that the theory of quantum mechanics was incomplete at that time, supported by the fact that he made the second assumption about the existence of hidden variables which were yet to be found
Summary
The application of entanglement concept is known to be predominant in quantum computers. This research focuses on three qubits based on the knowledge that the structures of the qubits are more complex and applicable in actuality This is due to the fact that in reality, quantum computers require more than three qubits to access data during high capacity information transmission. It is shown in the current recent, 20 qubits [1] and 50 qubits have been built and tested by IBM [2]. Entanglement became evident in the problem of quantum theory after Einstein, Podolsky, and Rosen (1935) [3,4,5,6,7] succeeded in describing the mysterious phenomenon inherent in quantum mechanics by initiating an experiment, known as the EPR paradox. It was reported that Einstein's assumptions were proven wrong when John Bell [8] succeeded in proving the existence of entanglement in an experiment conducted in 1964 [3, 8, 9]
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