We study the time evolution of quantum discord and entanglement of a two-qubit system in thermal reservoirs. We find that there are no simple ordering relations between entanglement and quantum discord for the dynamical evolution behavior; that is, quantum discord may be smaller or larger than entanglement in the evolution process. However, a strong correlation between changes of the ordering relations and the mean photon number is found. In addition, it also shows that entanglement is not the strongest form of nonclassicality. Considerable efforts have been devoted to study quantum correlations in the last two decades, mainly due to the general belief that they are a fundamental resource for quantum information processing tasks. Among them, entanglement is the most famous and best studied kind of quantum correlation and is generally regarded as a necessary resource in quantum computation and communication [1]. The situation started to change after a so-called DQC1 (deterministic quantum computation with one qubit) model was presented which may provide the speedup in the deterministic quantum computation with one pure qubit [2]. The fact is that no entanglement is present in this model; however, other kinds of nonclassical correlations are responsible for the quantum computational efficiency of DQC1. Such correlations are characterized as quantum discord [3], which is believed to be more general and more fundamental than entanglement [4–6] and which can be viewed as the amount of entanglement consumed in the quantum-state merging [7, 8]. Besides its application in DQC1, quantum discord has also been used in studies of quantum phase transition [9, 10], Maxwell’s demon [11], and relativistic effect [12, 13]. In addition, concerning biological systems, it has been suggested that such correlations could play an important role in photosynthesis [14]. In particular, quantum discord has been predicted to show peculiar dynamics under decoherence [15]. Considering two noninteracting qubits, it was shown that, under certain conditions, the decay rate of the correlations may suffer a sudden change [16, 17]. Furthermore, by analyzing various dissipative channels, some authors have shown that, in all cases where entanglement suddenly disappears, quantum discord vanishes only asymptotically [18–20]. In this sense, quantum discord is more robust against decoherence than entanglement so that quantum algorithms based only on quantum discord correlations may be more robust than those based on entanglement. Despite intense research over the last decade, the relation
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