Using Tsallis-
q entropy, we introduce the generalized concept of global quantum discord, namely the
q-global quantum discord, and provide its analytic evaluation for two classes of multiqubit states. We also provide a sufficient condition, for which the pairwise quantum correlations in terms of
q-global quantum discord is monogamous in multiparty quantum systems.
Due to some ambiguity in defining mutual Tsallis entropy in the classical probability theory, its generalization to quantum theory is discussed and, as a consequence, two types of generalized quantum discord, called
q-discords, are defined in terms of quantum Tsallis entropy.
q-discords for two-qubit Werner and isotropic states are calculated and it is shown that one of them is positive, at least for states under investigation, for all
q>0. Finally, an analytical expression for
q-discord of certain family of two-qubit X states is presented.