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Non-extensive statistical mechanics appears as a powerful way to describe complex systems. Tsallis entropy, the main core of this theory has been remained as an unproven assumption. Many people have tried to derive the Tsallis entropy axiomatically. Here we follow the work of Wang (EPJB, 2002) and use the incomplete information theory to retrieve the Tsallis entropy. We change the incomplete information axioms to consider the escort probability and obtain a correct form of Tsallis entropy in comparison with Wang's work.

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In this paper, the distinguishability of multipartite geometrically uniform quantum states obtained from a single reference state is studied in the symmetric subspace. We specially focus our attention on the unitary transformation in a way that the produced states remain in the symmetric subspace, so rotation group with J y as the generator of rotation is applied. The optimal probability and measurements are obtained for the pure and some special mixed separable states and the results are compared with those obtained at the previous articles for the special cases. The results are valid for linearly dependent states. The discrimination of these states is also investigated using the

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