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Entanglement conditions for mixed \(SU(2)\) and \(SU(1,1)\) systems. (English) Zbl 1140.81345

Summary: We derive a class of inequalities for detecting entanglement in the mixed \(SU(2)\) and \(SU(1,1)\) systems based on the Schrödinger-Robertson indeterminacy relations in conjugation with the partial transposition. These inequalities are in general stronger than those based on the usual Heisenberg uncertainty relations for detecting entanglement. Furthermore, based on the complete reduction from \(SU(2)\) and \(SU(1,1)\) systems to bosonic systems, we derive some entanglement conditions for two-mode systems. We also use the partial reduction to obtain some inequalities in the mixed \(SU(2)\) (or \(SU(1,1))\) and bosonic systems.

MSC:

81P68 Quantum computation
81S05 Commutation relations and statistics as related to quantum mechanics (general)
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