Nonlocality of three-qubit states of a nuclear spin-7/2

Abstract

Advances in quantum information processing can open a way for numerous applications of the processing in various fields of science and technology: communication, precision measurement, computing, nano-scale detectors, and sensors. Classical and various quantum correlations have been studied in real spin 1/2 systems. The nonlocality measures provide a novel classification scheme for bipartite states, highlighting that nonlocality is a quantum resource distinct from other types of quantum correlations. We first studied the temperature and field dependencies of nonlocality measure in the three fictitious spin 1/2 system, which represents a nuclear spin-7/2 placed in magnetic and inhomogeneous electric fields. The relationship between nonlocality and other quantum correlations (entanglement and geometric discord) was studied. The Hamiltonian and spin operators for a spin 7/2 are represented in the basis formed by the Kronecker products of the Pauli matrices. This transformation allows us to represent a spin 7/2 as a system of three coupled fictitious spins 1/2 and, from the quantum information point of view, as an equivalent system of three coupling qubits. Well-developed methods were used to calculate measures of quantum correlations. For example, we consider ⁵⁹Co (spin 7/2) in the compounds [Co(NH₃)₅Cl]Cl₂ and Ca₃Co₂O₆. The interaction between the fictitious spins of ⁵⁹Co nuclei depends on the magnitude and direction of the external magnetic field. Other potential cases of quantum correlations can be realized based on nuclear spins 7/2 in solid-state systems, for instance, such as ⁵¹V, ¹⁶⁵Ho, or ¹²³Sb.