Construction of four-qubit quantum entanglement for SI (S = 3/2, I = 3/2) spin system

In quantum information processing, spin-3/2 electron or nuclear spin states are known as two-qubit states. For SI ( S = 3/2, I = 3/2) spin system, there are 16 four-qubit states. In this study, first, four-qubit entangled states are obtained by using the matrix representation of Hadamard and CNOT logic gates. By considering 75 As@C 60 molecule as SI ( S = 3/2, I = 3/2) spin system, four-qubit entangled states are also obtained by using the magnetic resonance pulse sequences of Hadamard and CNOT logic gates. Then, it is shown that obtained entangled states can be transformed into each other by the transformation operators.