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Non-classicalities via perturbing local unitary operations

We study the nonclassical correlations in a two-qubit state by the perturbing local unitary operation method. We find that the definitions of various non-classicalities including quantum discord (QD), measurement-induced nonlocality (MIN) and so on usually do not have a unique definition when expressed as the perturbation of local unitary operations, so a given non-classicality can lead to different definitions of its dual non-classicality. In addition, it is shown that QD and MIN are not the corresponding dual expressions in a simple set of unitary operations, even though they are in their original definitions. In addition, we also consider the non-classicalities in general $2\otimes d$ dimensional systems.