Quantum discord in a three-spin system in an external magnetic field

We study quantum correlations in a bipartite heteronuclear $2{\times}1$ system with three spins $S=1/2$ in an external magnetic field at high and low temperatures. We analytically determine the minimum of the system conditional entropy at high temperatures after measurements on the one-spin subsystem for any relations between the spin frequencies of both subsystems. As a result, we obtain analytic expressions for the measure of quantum correlations, i.e., for the quantum discord in three-qubit systems, for the first time in the high-temperature case. We obtain the minimum of the low-temperature conditional entropy numerically. We investigate the quantum discord evolution and the relation between the classical and quantum correlations.