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In this paper, we give a sufficient and necessary condition (witness) for the sudden change of geometric quantum discord by considering mathematical definition of the discontinuity of a function. Based on the witness, we can find out various sudden changes of quantum correlation by considering both the Markovian and the non-Markovian cases. In particular, we can accurately find out critical points of the sudden changes even though they are not quite obvious in the graphical representation. In addition, one can also find that sudden change of quantum correlation, like the frozen quantum correlation, strongly depends on the choice of the quantum correlation measure.

The witness of sudden change of geometric quantum correlation