We investigate the dynamics and protection of quantum correlations of a qubit-qutrit system under local amplitude damping channels with finite temperature. The comparison between entanglement and geometric measure of quantum discord (GMQD) is analyzed. It is found that the GMQD is more robust than the entanglement against the decoherence induced by the channels. Special attention is paid to how to protect the quantum correlations from decoherence by weak measurement and measurement reversal. We find that the weak measurement is not necessary when the initial state is maximally entangled. But for other initial states, a successful protection of quantum correlations requires combined weak measurement and measurement reversal. Under certain conditions, we also notice that we can realize the protection at finite temperature for GMQD, but not for entanglement.

We study the thermal quantum correlations in terms of entanglement, quantum discord (QD) and local quantum uncertainty (LQU) in the XY spin chain, and analyze their capability in detecting the critical points of quantum phase transition. By considering the effects of the three-site interaction, site distance, system size and anisotropy parameter, we show that LQU is superior to QD in detecting the critical points. The advantages of LQU are not to be restricted to zero temperature, and it is possible to estimate the critical points at high temperature. Furthermore, the properties of LQU are very interesting and exhibit different quantum correlations which cannot be shown by entanglement and QD.

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