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We present a computable criterion for completely classifying multiqubit quantum states under local unitary operations. The criterion can be used to detect whether two quantum states in multiqubit systems are locally unitarily equivalent or not. Once a positive answer is obtained, we are further able to compute the corresponding unitary operators precisely. Since the scheme is based on the mean values of some quantum mechanical observables, it supplies an experimental way to judge the local equivalence of quantum states.
Li et al. (Mon,) studied this question.