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Quantum Discord and Entropic Measures of Quantum Correlations: Optimization and Behavior in Finite XY Spin Chains

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Lectures on General Quantum Correlations and their Applications

Part of the book series: Quantum Science and Technology ((QST))

Abstract

We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the associated optimization problem in qudit-qubit systems is shown to become feasible, allowing to approximate that of the quantum discord. As application, we examine quantum correlations of spin pairs in the exact ground state of finite XY spin chains in a magnetic field through the quantum discord and information deficit. While these quantities show a similar behavior, their optimizing measurements exhibit significant differences, which can be understood and predicted through the previous approximations. The remarkable behavior of these quantities in the vicinity of transverse and non-transverse factorizing fields is also discussed.

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Acknowledgements

The authors acknowledge support from CONICET (NG,NC,MC) and CIC (RR) of Argentina, and of CONICET grant PIP 11220150100732.

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Authors and Affiliations

  1. Departamento de Física-IFLP, Universidad Nacional de La Plata, C.C. 67, 1900, La Plata, Argentina

    N. Canosa, M. Cerezo, N. Gigena & R. Rossignoli

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  1. N. Canosa
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  2. M. Cerezo
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  3. N. Gigena
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  4. R. Rossignoli
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Correspondence to R. Rossignoli .

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Editors and Affiliations

  1. São Paulo State University, São Paulo, Brazil

    Felipe Fernandes Fanchini

  2. São Carlos Institute of Physics, University of São Paulo, São Paulo, Brazil

    Diogo de Oliveira Soares Pinto

  3. School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom

    Gerardo Adesso

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Canosa, N., Cerezo, M., Gigena, N., Rossignoli, R. (2017). Quantum Discord and Entropic Measures of Quantum Correlations: Optimization and Behavior in Finite XY Spin Chains. In: Fanchini, F., Soares Pinto, D., Adesso, G. (eds) Lectures on General Quantum Correlations and their Applications. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-53412-1_20

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