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Generalized quantum discord $(D_q)$, Einstein-Podolsky-Rosen steering $(S)$,entanglement $(E)$, and Bell nonlocality ($N$), are logically distinctquantifiers of quantum correlations. All these measures capture nonclassicalaspects of quantum states and play some role as resources in quantuminformation processing. In this work, we look for the hierarchy satisfied bythese quantum correlation witnesses for a class of two-qubit states. We showthat $N \triangleright S\triangleright E\triangleright D_q$, meaning thatnonlocality implies steering, which in turn implies entanglement, which thenimplies $q$-discord. For the quantum states under concern, we show that theinvariance of this hierarchy under noisy quantum channels directly implies adeath chronology. Additionally, we have found that sudden death of all quantumresources except discord is absent only for a subset of states of measure zero.At last, we provide an illustration of another consequence of theaforementioned hierarchy, namely, the existence of a sudden birth chronologyunder non-Markovian channels.

Generalized discord, entanglement, Einstein-Podolsky-Rosen steering, and  Bell nonlocality in two-qubit systems under (non-)Markovian channels:  Hierarchy of quantum resources and chronology of deaths and births