On the Stratifications of 2-Qubits X-State Space
1 A. Razmadze Mathematical Institute, Iv.Javakhishvili Tbilisi State University, Tbilisi, Georgia
2 Institute of Quantum Physics and Engineering Technologies, Georgian Technical University, Tbilisi, Georgia
3 National Research Nuclear University, MEPhI (Moscow Engineering Physics Institute), Moscow, Russia
4 Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia
Published online: 14 February 2018
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.
© The Authors, published by EDP Sciences, 2018
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