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Violation of Leggett-Garga's inequalities means that the system shows a type of non-classical correlation that exhibited by quantum observables measured at different moments of times. These correlations are used, for example, to test macroscopic realism, assess the "quantumness" of the system, and in the protocols in information theory. Despite well-established results regarding correlation in time for closed systems, the area of open systems is still poorly explored.