On the Stratifications of 2-Qubits X-State Space

The 7-dimensional family ℬX of the so-called mixed X -states of 2-qubits is considered. Two versions of stratifications of ℬX , i.e., its decomposition into strata according to orbit types of the adjoint actions of two groups, are described. The first stratification is due to the action of global unitary group GX ⊂ S U (4), while the second one corresponds to the action of the local unitary group LGX ⊂ GX . The equations and in-equalities in the invariants of the corresponding groups, determining each stratification component, are given.