Nuclear quadrupole resonance of spin 3/2 and entangled two-qubit states

A single spin-$3/2,$ possessing a quadrupole moment and placed in a non-uniform electric field, is isomorphic to a system of two spins of $1/2,$ which can be represented as two qubits. To create these qubits, the degeneracy of the energy levels is removed by applying two radio-frequency fields with different phases and directions. The properties of entanglement between two qubits are studied. We analyze the concurrence, the entropy of entanglement, and fluctuations of the entropy in the pure and mixed states. Concurrence and entropy of entanglement in a mixed state increase with decreasing temperature and approach to their values in a pure state. For a nucleus Cu in high temperature superconductor ${YBa}_2{Cu}_3{O}_{7-\delta },$ the estimation of the temperature, at which entanglement appears, gives $T⩽$ 0.8 μK. (paper)