Quantum Inf Process (2013) 12:205–215 DOI 10.1007/s11128-012-0367-x Construction of four-qubit quantum entanglement for SI(S = 3/2,I = 3/2) spin system Ahmet Gün · Selçuk Çakmak · Azmi Gençten Received: 22 April 2011 / Accepted: 27 January 2012 / Published online: 8 February 2012 © Springer Science+Business Media, LLC 2012 Abstract 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. Keywords Four-qubit states · Four-qubit CNOT · Quantum entanglement · Endohedral fullerenes · Magnetic resonance selective pulses 1 Introduction A unit of information in quantum information processing (QIP) is called quantum bits (qubit in short) [1–3]. Qubits can be represented by the two states of any quan- tum system such as spin states of nuclei, an electron’s orbital states in an atom or photon polarization states. Quantum entanglement is essential for some appli- cations of QIP such as superdence coding, quantum cryptography and quantum A. Gün · S.Çakmak · A. Gençten (B ) Department of Physics, Faculty of Arts and Sciences, Ondokuz Mayıs University, 55139 Samsun, Turkey e-mail: gencten@omu.edu.tr A. Gün e-mail: agun55@hotmail.com S.Çakmak e-mail: cakmak.selcuk@gmail.com 123