Quantum and classical correlations in three-qubit spin

Abstract

The Hamiltonian and the spin operators for a spin $$ \tfrac{7}{2} $$ are represented in the basis formed by the Kronecker products of the Pauli matrices. This allows us to represent eight quantum states of the spin 7/2 as the states of three coupled fictitious spins $$ \tfrac{1}{2}, $$ which can be considered as a system of three coupling qubits. The Hamiltonian for the three-spin system contains terms describing bi- and tripartite interactions with the strengths depending on the asymmetry parameter of the electric field gradient and the applied magnetic field. This leads to unusual magnetic field dependences of the classical and quantum correlations between the fictitious spins. It is shown that, unlike the predictions of the Ising, Heisenberg, and dipole–dipole coupling spin models, the quantum mutual information, classical correlations, entanglement, and quantum discords between the fictitious spins do not vanish with an increase in magnetic field. (The correlations tend to their limit values in a high field.) All the correlations possess the minima in the field dependences. The tripartite concurrence can achieve the maximal concurrence in a three-spin system in the pure state. The proposed approach may be useful for analysis of properties of particles with larger angular momentum and the many-body interactions.