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Geometrical description of the dynamics of entangled two-qubit states under \(U(2) \times U(2)\) local unitary operations

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Abstract

We realize the second Hopf fibration for a two-qubit system without using the quaternionic language. In this respect, we explore the geometrical features emerging from this Hopf fibration. Further, we investigate the metric tensor and the SO(4) non-abelian gauge field defined on the \(S^4\)-base in terms of the entanglement quantified by the Wootters concurrence on the associated Hopf bundle. Finally, by transforming an entangled two-qubit state in the Schmidt form, we examine the different quantum phases acquired by this state under \(U(2) \times U(2)\) local unitary operations in relation to the entanglement as well as the geometry of the corresponding state manifold.

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Authors and Affiliations

  1. LPHE-Modeling and Simulation, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco

    Brahim Amghar

  2. Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera, 11, 34151, Trieste, Italy

    Mohammed Daoud

  3. Department of Physics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco

    Mohammed Daoud

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  1. Brahim Amghar
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  2. Mohammed Daoud
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Amghar, B., Daoud, M. Geometrical description of the dynamics of entangled two-qubit states under \(U(2) \times U(2)\) local unitary operations. Quantum Inf Process 20, 389 (2021). https://doi.org/10.1007/s11128-021-03341-4

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