Using measurement induced disturbance to characterize correlations of multipartite non-k-classical states

In [S. L. Luo, Using measurement induced disturbance to characterize correlations as classical or quantum, Phys. Rev. A77 (2008) 022301], the author presented a statistical correlation measure for bipartite quantum states using measurement induced disturbance. In this paper, motivated by this correlation measure, we obtain some necessary conditions for [Formula: see text]-classical states in multipartite quantum systems, and obtain a relation between the set of [Formula: see text]-classical states and the set of [Formula: see text]-product states; Secondly, we introduce a class of correlation measures based on trace distance using measurement induced disturbance in order to quantify the strength of correlation for non-[Formula: see text]-classical states; Lastly, we introduce the concept of quantum channel with respect to [Formula: see text]-partition, it is simply denoted by identical-[Formula: see text]-channel, and furthermore discuss the influences of the correlation measure under identical-[Formula: see text]-channel.