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Nonlocality threshold for entanglement under general dephasing evolutions: a case study

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Abstract

Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, a closed formula of the Bell function, witnessing nonlocality, as a function of the concurrence, quantifying entanglement, valid for a system of two noninteracting qubits initially prepared in extended Werner-like states undergoing any local pure-dephasing evolution. This formula allows for finding nonlocality thresholds for the concurrence depending only on the purity of the initial state. We then utilize these thresholds in a paradigmatic system where the two qubits are locally affected by a quantum environment with an Ohmic class spectrum. We show that steady entanglement can be achieved and provide the lower bound of initial state purity such that this stationary entanglement is above the nonlocality threshold thus guaranteeing the maintenance of nonlocal correlations.

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Acknowledgments

R.L.F. would like to acknowledge Gerardo Adesso and his group at the University of Nottingham for the very kind hospitality during the completion of this work. R.L.F. also thanks Sigur Rós for fruitful meetings.

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  1. Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, Università di Palermo, Viale delle Scienze, Ed. 9, 90128, Palermo, Italy

    Rosario Lo Franco

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  1. Rosario Lo Franco
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Lo Franco, R. Nonlocality threshold for entanglement under general dephasing evolutions: a case study. Quantum Inf Process 15, 2393–2404 (2016). https://doi.org/10.1007/s11128-016-1290-3

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