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On the stratifications of 2-qubits X-state space

Abstract

The 7-dimensional family PX\mathfrak{P}_X of so-called mixed X-states of 2-qubits is considered. Two types of stratification of 2-qubits Xβˆ’X-state space, i.e., partitions of PX \mathfrak{P}_X\, into orbit types with respect to the adjoint group actions, one of the global unitary group GXβŠ‚SU(4)G_X \subset SU(4) and another one under the action of the local unitary group LGXβŠ‚GXLG_X \subset G_X, is described. The equations and inequalities in the invariants of the corresponding groups, determining each stratification component, are given

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