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The 7-dimensional family $mathfrak{P}_X$ of so-called mixed X-states of 2-qubits is considered. Two types of stratification of 2-qubits $X-$state space, i.e., partitions of $mathfrak{P}_X,$ into orbit types with respect to the adjoint group actions, one of the global unitary group $G_X subset SU(4)$ and another one under the action of the local unitary group $LG_X subset G_X$, is described. The equations and inequalities in the invariants of the corresponding groups, determining each stratification component, are given.
The moduli space of Higgs bundles has two stratifications. The Bialynicki-Birula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises from the Harder-Narasimhan
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