Emergence of maximal hidden quantum correlations and its trade-off with the filtering probability in dissipative two-qubit systems

We investigate the behaviour of quantum CHSH-nonlocality, F3-steering, and usefulness for teleportation in an interacting two-qubit dissipative system. We show regimes where these three quantum correlations can be extracted by means of local filtering operations, despite them not being displayed in the bare natural time evolution. Moreover, we show the existence of local hidden state (LHS) and local hidden variable (LHV) models for some states during the dynamics and thus, showing that apparently-useless physical systems could still exhibit quantum correlations, which are hidden from us, but that can still be revealed by means of local filtering operations and therefore, displaying the phenomenon of hidden quantum correlations. Furthermore, we report on extreme versions of these phenomena, where the revealed correlations achieve the maximal amount allowed by quantum theory. This phenomenon of maximal hidden correlations relies on the qubits collective damping, and may take place even in long-distance separated qubits. Despite the immediate appeal of the physical system displaying such an extreme phenomenon, we furthermore show however, that there actually exists a trade-off between the amount of quantum correlations which can be extracted and the filtering probability with which such protocol can be implemented. Explicitly, the higher the amount of correlations to be extracted, the more difficult it becomes for the protocol to be implemented (lower filtering probability). This is consequently showing us the remarkable fact that whilst the phenomenon of maximal hidden quantum correlations does naturally emerge during the evolution of physical systems, Nature does not completely give it away for free, by imposing a limit to the rate at which this can be done. From a theoretical point of view, the existence of such trade-off imposes a fundamental limit to the extraction of quantum correlations by local filtering operations. From a practical point of view on the other hand, the results here presented determine the amount of resources that should be invested in order to extract such maximal hidden quantum correlations.